The items for Break HP/Damage on the characters special dressspheres are:

For Yuna's Floral Fallal

Break Damage - The item "Twilight Rain". Can be found in Chest in Waterfall Way in Besaid (not sure how you get to this, sorry).

Break HP - The item "Aurora Rain". Can be found in a chest in the Chamber of the Stolen Fayth.

For Rikku's Machina Maw

Break Damage - The item "Machina Booster". Can be found in a chest in the HQ - lift of Mushroom Rock Road.

Break HP - The item "Machina Reactor". Can be found in a Chest in the Chocobo Dungeon.

For Paine's Full Throttle

Break Damage - The item "Victor Primoris". Can be found in a chest in Mi'hen Highroad New Road North Entrance (I think for this you ride a chocobo and stand on a yellow feather until it asks you if you want to jump).

Break HP - The item "Corpus Invictus". Can be found in the New Cave in the Thunder Plains.

For more details on getting these, you'll have to look on Game FAQs, I am looking at the strategy guide and this is all it says really =)