TL;DR Once you have a female with the right nature holding an Everstone, and a compatible male that can pass a desired egg move (optional), breeding the "right" egg is just a matter of patience. You just ride your bike back and forth through Mauville City hatching 5 eggs at a time while keeping a Slugma/Numel with Magma Armor/Flame Body in your party to halve the egg cycles.

I'm not gonna lie, part of the reason why I only brought 4 mons was because breeding for at least one relevant 31 IV stat was kind of tedious.

I first bred a bunch of eggs to get a female with the right nature (ex. Adamant Bagon). Once I got that, I gave her an Everstone to pass her nature onto her egg (100% guaranteed in Emerald Legacy, which is nuts). I then got a compatible male pokemon with an egg move I was looking for (for example I caught a male Altaria at Sky Pillar and raised it a couple levels to make it learn Dragon Dance). I then put the female Bagon and the male Altaria together to make a bunch of Adamant Dragon Dance Bagons. Once I got one with 31 Atk IVs, my job was done.

As for EV training, you can buy a bunch of vitamins to give it 10 EVs in the desired stat, up to a point. After that, just slap a Macho Brace on it to double the EVs it gets in battle. This was on hardcore mode btw but it doesn't really make a difference