So I've recently decided I want a shiny Tyrunt and Tyrantrum in ORAS. I've gotten the shiny charm, a foreign ditto, and have been working on breeding for a good while.

But I've been filling my boxes pretty fast (only 3, but that's still fast enough to know I'm not going to like how long it takes to get results), and I'm wondering how you guys deal with, as much as I dislike the term, failures? I'm not looking to breed for IVs, just a couple shinies. Any advice would be welcome.

I used this trick when hunting for Munchlax in Platinum - it doesn't do anything about your full boxes, but it does give you a good idea of your estimated time until Shiny encounter.

From GenVI onward, the Masuda method gives probability of 1/638 for Shiny occurrence. To estimate the number of attempts when the odds of you having hatched a Shiny by then are 1/2 or 50% (past which point you should be increasingly likely to encounter one), you use the following formula:

(637/638)^x = 0.5

Plugging into Wolfram Alpha and solving, we can find that your odds of having at least one Shiny Tyrunt reach 50% after 442 attempts. Assuming a Box limit of 30, this means you'll be using just under 15 of your Boxes if you don't release a single Tyrunt and don't encounter a single Shiny until exactly the 50% mark.

Personally, I found a Munchlax when the odds of finding one (using this math) had reached about 40%, so don't expect much until you get close unless you're lucky. It seems hopeless at first, but keep at it - something like 6 hatches a day should get you there in about two and a half months.

Also, I'm not extremely familiar with professional breeding - is there any reason you aren't releasing them?

7450129
It just seems like a waste, but wonder trading is a crap show and regular gts is only one at a time in ORAS. I may keep a box or two as trade fodder for when I finally move over to Sword (on a pokemon journey through all the generations right now, which allowed me the shiny charm in the first place).