The two above make good points, but here's the info just in case you want it.

There are four ways to Break HP Limit in this game.

1. Enterprise
You get this by skipping the Moonflow mission in Ch 1. If you do this, you will get a scene with Tobli in Kilika, and he will be on the Celsius at the start of Ch 2 along with the other band members. When you have to push all of them into the elevator, if you can also push Tobli into the elevator (pain the ass to do) you will be rewarded with the Enterprise accessory.

2. Higher Power GG
To get this, you must clear the secret dungeon in the Chocobo Ranch. After you beat the Anything Eater, there's a scene with Clasko, then you get Higher Power.

3. The End GG
To get this, you must oversoul every single oversoulable fiend in the game. Once you've done this, check your bestiary, and Shinra will give you The End.

4. Special Dress Spheres
Each girl has an item to find the will give her the ability to learn Break HP Limit as an ability for her special dress sphere.

Flora Floral - Aurora Rain
You get this in the chamber of fayth where Yojimbo once was slept in Ch 5.

Machina Maw - Machina Reactor
You find this in a chest in the Chocobo Ranch dungeon in Ch 5.

Full Throttle - Corpus Invictus
You find this in the Thunder Plains hidden cave in Ch 5.

The GGs are the way to go, since every girl can use it at the same time.