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According to Bulbapedia, the only NA release of Mew in Gen III have their OT fixed (Aura or MYSTRY)
NA didn't have the Old Sea Chart event item released, so Emerald players cannot capture their own Mew. (Japan had theirs released)
I have a box of 5IV xAttack Modest Bulbasaur eggs that I've saved. I plan to give these eggs away after I check my remaining (400+) eggs for shinies. Should I save more eggs, or release the remaining xAttack hatched babies? Are they 'in demand' as far as giveaways go?
After a quick read, the baby inherits two IVs of the opposite gender parent (or ditto if it's used). The defense IV is always inherited as is, while the special IV has a 50% of being inherited as is, and the other 50% inherited plus 8 (then modulo 16). Attack and speed IVs are random, and HP IV...
Even with Shiny Charm, it can take a long time to breed a flawless shiny. That's quite a tall order. Your best bet is probably preparing some flawless eggs, and getting their SV checked in the SV thread. Good luck.