I hope this info that i found on a wabbie helps:

To earn your Limit Breaks:

Level 1, first break:
- You start with this one already.

Level 1, second break
- Use your first break of that level 8 times.

Level 2, first break
- Kill 80 enemies. Your character has to be the one to deliver the killing blow in order to have it count. You can kill an enemy in any way (spell, Morph, use an item, etc.) Vincent only has to kill 60 enemies in order to fulfill this requirement.

Level 2, second break:
- Use your first break of that level 6 times.

Level 3, first break:
- See 'Level 2, first break' notes.

Level 3, second break:
- You must use your first break of that level 4 times.

Level 4, extreme limit break:
- Learn all your character's other Limit Breaks (6 for everyone but Cait, 3 for Vincent). Then use your character's Limit Break Manual on that person.

Omnislash - To gain this awesome limit break, you must have gained it from the Battle Square in the Gold Saucer.

I suggest giving your character the Slash All materia or some spell that injures all enemies when trying to learn your first break for each new level. Try to find an area where you can fight many, easy to kill enemies at once (like near Mideel).

As for second breaks, try using a Hyper on the character whose break you want to learn, then give them a Cover materia so they'll take more damage and consequently have their Limit Break bars fill faster. If you're really desperate, give them a weak bracelet and a weak weapon so that they'll take more damage and be able to use their break more times without killing their opponent per battle.

To be able to use a limit break manual level 4, you must have learnt all the other limit breaks for that character, but you can still have the manual.

(Final Fantasy Worlds Apart)