After talking about the Demon Slayer Corps, Demons, and Muzan's forces, or at least part of each since Sakonji didn't trust her all that much and wasn't about to reveal too much to her, Pinkamena found that he brought her out to part of his place, his mountain, that was away from the house, before stopping as he turned to face her, revealing an area that was full of bamboo. While he didn't trust her, even though she hadn't eaten anyone and had no desire to eat Humans, he did show her a few movements that were tied to his style of Breathing, which he did confirm was the Water Breathing as she had guessed based on his personality, even though he was able to perform the motions without a blade, showing her how skilled he was. Such a thing told Pinkamena that Sakonji had to be a retired Hashira, because based on everything she had seen so far he was far more than an ordinary swordsman, though she wasted no time in drawing the blade she was being lent and took up a stance identical to what he was showing her right now, where she attempted to replicate everything he had shown her, or at least the first couple of steps. His technique was to swing along with the blade, that the position of the blade and the direction one applies the force of the swing in had to be the same, causing her to raise an eyebrow before shrugging as she followed his teachings, figuring that she had no knowledge on how to use a weapon and watching him was the best bet for her right now.
There was also a slight threat added to everything he taught her, that normal blades could be worn down with time and that the user had to be careful, because if their blades broke then the user's body would break as well, a warning to make sure those he taught were careful during his training, though given her demonic abilities she didn't have to worry about such a thing happening. Of course she did take the warning to heart, since there was no telling how durable the blade she had been given was, and moved through the motions that Sakonji showed her, pausing every now and then as he correct her stance or made some alteration to her body, where she followed his suggestions as she practiced using the blade. Another thing she found was that she wasn't getting tired at all, which she figured had to be part of the unlimited stamina and endurance, meaning she could train for a long period of time without having to rest at all, meaning that, while Sakonji was standing nearby and often corrected her stance, he slowly found that she was improving over time and he didn't need to step in as often as he thought he might. Pinkamena was sure that her mentor's plans had been designed based on the fact that she didn't remember anything from her 'Human life', so in his eyes he figured that he would have stepped in far more than what was currently happening, but he was still watching her and making sure she wasn't a threat to him and Tanjiro, not to mention the Humans they had seen on the way to this mountain.
Another thing Sakonji did was pull her aside and beckoned for her to attack him, where Pinkamena discovered that her mentor decided to use no weapons and grabbed onto her with his bare hands when she tried to swing at him, finding that he was able to launch her in whatever direction he wanted, training that was designed to make one roll and get back up onto their feet without wasting time, or hooves in her case, since fighting Demons was a matter of life and death and her movements could decide her fate.
"Hey, Sakonji... won't you get in trouble for training a Demon?" Pinkamena asked, choosing to do so during one of the few moments that he actually allowed her to stop, not that it mattered since her new abilities allowed her to continue without needing a break and it was more for him to relax before starting the next set of movements, "I understand that you might be a former Hashira, but won't the Corps be mad at you for doing this?"
"Possibly. However, you aren't like all of the other Demons we've seen so far... I'm honestly not sure what the Hashira will do once they learn about you," Sakonji replied, which was the truth, as she was different from all of the foul Demons they had slain since the organization had been founded, especially given the fact that she seemed capable of walking in the sun at all times, which needed to be kept from Muzan at all times, though as he said that Pinkamena reached behind a tree for a moment and pulled out an arm of the Demon that Tanjiro had encountered.
"What? Don't look at me like that." Pinkamena said, where she tore into the arm and ate part of it, finding that Sakonji did tilt his head for a moment, like he was disappointed in her or something, though she found that part of her power seemed to influence the area around her, keeping her food from burning in the sunlight, "You said Demons need to feed, least they grow weak and everything, but since I have no desire to eat Humans, as it will cause both you and the Demon Slayer Corps to come after me, that leaves the Demons who have been slain."
"But... Demons turn to ash when they're slain..." Sakonji stated, where this was another thing that surprised him, given that he had seen the death of the Demon whose arm Pinkamena was devouring, making sure not to bother him by moving off to the side of the clearing they were in, though he suspected that she had developed her own Blood Demon Art, a power that was unique to her since every single Demon was different from each other.
"Well, I didn't, and neither does my food." Pinkamena replied, though she refrained from adding something to that, as she found that while she could access the storehouse from this world, without having to actually travel to her hidden world at all, anything that was removed from whatever was inside the first structure replaced itself, confirming that she now had an unlimited amount of food, before she finished off the arm and caused the bone to disappear.
Sakonji said nothing to that as Pinkamena got up and returned to her training, swinging the blade as she had seen him do at the start of this, unsure as to what he was supposed to do since his own teachings told him to cut her down and put an end to a potential Demon that might cause headaches for the Corps, while his feelings were to stay his hand and watch all of her movements before making a decision. While she trained he excused himself for a short period of time, giving him a chance to slip back to his hut and take up his writing materials once more, where he composed two messages this time, as one was for the individual who sent Tanjiro and Nezuko his way, the other was for the head of the Corps, as he needed to know about Pinkamena's existence. He wanted a second set of eyes on this situation, someone to talk to while Tanjiro was in the middle of his training, before the odd Demon was sentenced by the Hashira and their leader, though knowing who was in charge of the Corps he might see this as a good thing and ask that she come speak to him before taking part in the Final Selection, no doubt to gauge her with his own eyes. Plus there was a chance that she might snap and attack them, as in him and Tanjiro, not to mention whoever might be near this mountain, so having a Hashira nearby for a few days might be enough to calm his nerves and see if Pinkamena was as different as she claimed she was, just in the off chance that this was a way for Muzan to kill the Corps without drawing attention to himself.
Once he was done with his letters, and made sure that Pinkamena was still swinging her blade while Tanjiro slept, he took a moment to carefully call down two crows, a special species that the Corps used for communication, and gave them their letters, one heading out to seek out the Hashira he was conversing with and the other heading for their leader's position, where the latter would take some time since it moved every now and then.
While he did that Pinkamena continued her training, swinging the blade like she had seen as she considered some things, even though it was mostly the fact that she was sure that the Corps would have a hard time accepting someone like her into their ranks, before she paused for a moment when she noticed that Sakonji hadn't returned yet and glanced down at her hand. Part of her was curious as to whether or not her power, Chaos World, would allow her to alter other things, such as make those who gazed upon her see a Human and not a Demon, something she was going to have to experiment with in the future, before sighing as she resumed swinging her blade as she imagined that this was a fight against enemies and not against the open air. Of course she noticed a pair of crows fly towards the hut and leave it not a few moments later, all while carrying what appeared to be letters wrapped around one of their legs, so two letters, before separating from each other and heading in different directions, meaning Sakonji was likely telling someone about her and how odd she was, in comparison to all the other Demons of this land. She was interested in what have been written on the letters, but, even if that was the case, she wasn't about to stop her training and hunt them down so she could learn what Sakonji wrote on the pair of letters he was sending out, hence why she focused on her training and nothing else, to improve her offensive and defensive powers for whatever the future held for her.
As it turned out it was the following day when Tanjiro started his own training, as Sakonji gave him the first day off, mostly to allow him to rest and recover from what had happened so far, namely running to this mountain and then the test that was on another part of the mountain, though it seemed that Sakonji planned on having Tanjiro focus on his endurance and stamina first, before worrying about his blade. One thing Pinkamena discovered was that the Cultivator had several training blades for them, which made sense considering that he and the others might train more than one person at any given time, as they could train four, maybe five, possibly even ten if they wanted, so having training blades at the ready made sense to her as she continued her own training. Of course she also spent some days following Tanjiro, mostly due to the fact that Sakonji wanted someone to keep an eye on him and collect some information on him so he could rapidly add new challenges, even though she was sure that the man had some ideas on what to do and didn't need her to do such a thing, but she kept silent and aided him to the best of her new abilities. Even though her stamina and endurance were far beyond Tanjiro's, meaning the mountain descent training was useless for her, Pinkamena tried a few of them out, just to see what her companion was dealing with everyday, before sticking to running along the treetops and watching him fall for certain traps while completely overcoming others.
Whenever Tanjiro took a break he would often speak with her before resuming his own training, talking about his family, the village they had lived near, his father and the Hinokami Kagura, a dance that they had offered to the Fire God at the start of every new year to ward of both threats and diseases, the fact that his Hanafuda earrings were part of the dance and were passed from father to son, and other things. When Pinkamena thought about it, and listened to the explanation as to what the dance was, she was positive that it sounded like another Breathing Style, which she wasn't sure of since she had no knowledge of how many there were in this world, but she kept that information to herself as Tanjiro trained, just to make sure his focus was on his own training. Sometime after that Sakonji had Tanjiro start training with his own blade so he could get used to the weight of it, which only decreased his chances of success in dodging traps, which annoyed him whenever it happened, and it seemed that talking to her seemed to allow him to calm down and focus on his training, a fact that she was fine with since it gave her more information to work with. She also learned that the Hinokami Kagura had twelve named forms for a practitioner to use, those being Dance, Clear Blue Sky, Raging Sun, Burning Bones Summer Sun, Setting Sun Transformation, Solar Heat Haze, Beneficent Radiance, Sunflower Thrust, Dragon Sun Halo Head Dance, Fire Wheel, Fake Rainbow, and Fire Dance, which Tanjiro demonstrated one at a time.
It was an interesting dance, and she was sure that it was a hidden Breathing Style, but she said nothing as Tanjiro focused on his training, as with the addition of the blade he had to swing it after descending the mountain, a thousand swings to be exact, which Sakonji altered accordingly, usually adding more to make sure his arm strength was at it's peak, and he even knocked Tanjiro into a lake near a waterfall, why Pinkamena had no idea and she wasn't about to question it.
A few things happened as the days turned into weeks and the weeks turned into months, as at the end of their first month on the mountain Pinkamena noticed a figure watching them, not Sakonji based on what she was seeing, as this one was a younger male who wore a serious and emotionless look on his face, who wore a black uniform of some kind, like the attire of a Demon Slayer, with a haori that seemed to be made out of two different ones, the right being solid red while the left half had squares of green, orange, and yellow. She was sure that the figure was someone of importance to the Corps, as in one of the Hashira, and that meant that Sakonji wanted a second set of eyes to watch her for a time, hence why she kept practicing the movements she had been shown while finding that they came to her much faster as she practiced them, to the point where she confirmed that this training was for the Water Breathing style. It was obvious when she considered all of Sakonji's motions and some of his speech patterns, as he was trying to hammer all that information into Tanjiro, whose focus was on getting revenge on the Demon who killed most of his family and turned Nezuko into a Demon, though their mentor did seem pleased that someone understood his training. Of course she continued her training into the night, due to the fact that she didn't need to sleep all that much, and made sure to be a good distance away from Sakonji's place as she did it, just to make sure the sounds of her training didn't bother them while they were sleeping and preparing for the next day's events.
The Hashira who watched her disappeared after the first time she noticed him, no doubt heading out to fulfill his duties to the Corps, though she was sure that he returned every now and then to watch over her for some time, just to make sure nothing changed with her, though she pushed that out of her mind as she focused on the training she was undergoing, as the movements were interesting and gave her some ideas.
When the sixth month started, however, Tanjiro and Sakonji noticed that Nezuko, who had been sleeping for the most part and hadn't come out of the hut since their arrival, had fallen into a deep sleep, as if she might have lost consciousness and it worried her brother to no end, even though it did give Pinkamena a chance to actually see Tanjiro's demonic sister with her own eyes. Nezuko was a petite young girl, who was twelve according to her brother, who had long black hair that just so happened to reach her waist and the ends were flame red colored, due to her demonic nature since Tanjiro stated that it had been black before the transformation, who wore a light pink kimono that had an interesting flower pattern on it, or at least Pinkamena thought so. There were a few other additions, like the bamboo gag that her fangs were biting into right now, mostly to prevent her from attacking and eating people, and she found a small pink ribbon in her hair, the left side to be exact, though right now she seemed to be peacefully sleeping, likely unaware of what was happening around her, but it didn't stop Tanjiro from making sure to maintain a journal, just for her. Of course Sakonji also called for a doctor to come, one that had to be part of the Corps since he couldn't let just anyone come and see Nezuko, though they found nothing off about her and went about their business like usual, no doubt returning to tending to the other Demon Slayers who might be in this region, allowing Pinkamena and Tanjiro to return to their training.
Following that Tanjiro dedicated himself to his training, pushing his body to the extreme by heading into the highest parts of the mountain, as in those that had a lack of oxygen to condition himself for later, which he did for six more months, in addition to his sword training, before Sakonji approached them, as Pinkamena was offering Tanjiro some pointers, even if he was oblivious to some aspects of this.
"Tanjiro... I have nothing more to teach you," Sakonji said, something that caused Tanjiro to pause for a moment, due to the fact that he had poured himself into his training and this wasn't something he was expecting to hear, to which he took a moment to beckon for them to follow him as he walked towards another part of the mountain, "from now on you'll have to prove yourself, by improving on the basics that I've taught you so far. I will allow you to join the Final Selection... but first you need to cut this boulder in half."
The area he brought them to happened to be a clearing, one that looked like it had been prepared ahead of time, likely the moment that Tanjiro appeared on his radar, and in the middle of it rested a large boulder with a rope ring located right in the area one's neck would be in, though as Tanjiro realized the absurd nature of this request Sakonji lead Pinkamena over to another clearing, one some distance from the young boy and happened to have an identical boulder inside it.
"I know you'll likely break this in no time, but it's a requirement of my training," Sakonji continued, where he created this to make sure Tanjiro didn't get an idea of what to do, though as he said that he stood near some of the bamboo and watched as Pinkamena approached the boulder, no doubt studying it for a few moments as she considered her options, "however, I had to split you up..."
He never finished his statement as Pinkamena shifted her stance and gripped the handle of her blade, breathing like what a master of the art would do, before she shimmered for a moment as she drew it and advanced on the large boulder that was in front of her, where he found that water actually gathered around her blade as she danced around her target, which allowed her to deliver a number of slashes to the boulder before she reappeared near him and sheathed the blade not a few seconds later, breaking the rock into a thousand pieces.
"Water Breathing, Third Form: Flowing Dance..." Sakonji commented, as that was beyond what a normal practitioner would do when wielding his particular type of Breathing, because normally one would imagine the water around their blade while they fought their enemies, as there was no magic involved in their techniques, but with Pinkamena the impossible had, in an odd twist, become possible, "So, you have completed your training... as odd as it sounds... which means it's time for you to head to the Final Selection and survive the final test before becoming a Demon Slayer."
"Not yet... there's something I need to work on," Pinkamena said, as while she was pleased that she had replicated one of the ten techniques that belonged to the art of Water Breathing, and could possibly do the same with the other nine, part of her wanted to see if there was something else she could do before heading to the Final Selection, hence why she took a moment to glance over in Tanjiro's direction, who hadn't cut through his boulder yet.
Pinkamena found that Sakonji was fine with this and allowed her to continue with her work, where she used the clearing as a new practice area as she tried new movements and techniques, as she wanted to know more about how to wield the blade that was in her possession, mostly to make sure her chances of succeeding in her mission were boosted, all while Tanjiro continued to fail in his task. He spent the next six months trying to overcome the boulder that had been prepared for him, be it practicing his swings on the bamboo and empty air, rereading his journals to see if his notes contained some sort of clue as to what he was supposed to do, running up and down the mountain to improve every aspect of his body so he would be in peak form, and resting near Nezuko every night. It was kind of sad, if she was being honest with herself, as she felt that Sakonji's training was rather simple in some places and difficult in a few other spots, but it wasn't hard to the point where she was in Tanjiro's position, and she would have given him some pointers if Sakonji hadn't told her to let him find his own path. Other than that nothing happened and she found that no Demons seemed to come this way, no doubt due to some sort of incense the Demon Slayers used to keep themselves hidden, or maybe the Hashira kept this place safe for his mentor to teach those he accepted as his pupils, allowing them to focus on their training as she silently developed a few new moves, in a style that was different from Sakonji's.
Things got interesting when Tanjiro, on the verge of admitting defeat, was visited by a pair of spirits, as Pinkamena could see that they weren't physical for the most part, save for when a young male wearing a fox mask, who had something on that looked like the yellow and green part of the Hashira's haori, swung at him and their blades collided with each other, or the bamboo blade hitting his metallic blade. From what she could see the spirit seemed to think that Tanjiro was weak and that he didn't have what it took to be a Demon Slayer, though she refrained from jumping in since this seemed to be what Tanjiro needed, as the sudden arrival of a foe, who could do what he couldn't, might snap the lessons into place, hence the reason she merely watched them. Of course there was another spirit, a young girl with another fox mask, which she had to assume was a signature of those who put themselves through this sort of training, who wore a sleeveless haori and a red yukata, a shirt basically, appeared near her and tended to Tanjiro whenever the other spirit was done with his training, all while learning that the female was called Makomo and the male was Sabito. Makomo was more of an educational teacher, explaining everything to Tanjiro in a way that he could understand it, and he did with a decent speed, while Sabito was the instructor who put everything together with experience, challenging Tanjiro to form the techniques that Sakonji had taught him and use them as they were intended, even if it started with smashing the boulder.
Even with all the assistance it took Tanjiro some time to get the hang of things, half a year to be exact based on her count of the days and Sakonji explaining the calendar to her, allowing him to grow out his hair and learn what he needed so he could challenge Sabito, who accepted and came to the match with a real sword, though it ended with Tanjiro scoring the first strike, where he cleaved Sabito's mask in half... and when he came back to his senses both spirits were gone, though he was successful in cutting his boulder, meaning he was ready for the Final Selection and whatever the world had to throw at them.