break hp and mp limit

To break HP limit you will need an item called Wings To Discovery. You can get 30 of them from the chocobo race under the Remiem temple in the Calm Lands but after that the only other way to get them is to bribe marlboros a lot of gil. For break MP limit you need the Three Stars item. You can bribe the behemoth King for these.

Wings to Discovery, used for Break HP Limit, can be obtained by doing what gamespro said and also by defeating Shinryu in the Calm Lands Arena. And for Break MP Lmit, you need Three Stars, which can be obtained by bribing Behemoth King inside Sin and defeating Catoblepas aslo in the Calm Lands Arena. Also if your characters are strong enough, Ultima Buster sometimes drops shields with Break MP Limit and Nemesis( I think is how you spell it) sometimes drops Break HP Limit( as well as Break Damage Limit). I've heard that Yojimbo's Zanmato works on them both but I have yet to try this. Hope I helped