OK, about the chocobo dungeon. You need to send out 5 chocobos per level, 1 through 5, and have them all return to you. So that's 5 level 1 chocobos, 5 level 2 chocobos, 5 level 3 chocobos...and so on.
The accessory that bestows Break Damage Limit is the Invincible. You need to go to Kilika and talk to the camera man on the ship (the one who asks you if you'd like to see the Youth League HQ) and accept his offer. You must do this in Chapter 1 and 3. Talk to him again in Chapter 5, agree to have another look, then agree to go over to the island. The Invincible is in a chest on that island. Use the map to help you navigate.
