Barret's limits are as follows:
Lv. 1 Limits
Big Shot (default)
Mindblow (use Big Shot 9 times)
Lv. 2 Limits
Grenade Bomb (kill 80 enemies while on Lv. 1 Limit)
Hammer Blow (use Grenade Bomb 8 times)
Lv. 3 Limits
Satellite Beam (kill 80 enemies while on Lv. 2 Limit)
Angermax (use Satellite Beam 6 times)
After that you can learn his Level 4 limit, Catastrophe, once you find it.
It can be found in Corel in the other house other than the Inn. Do note that you can only obtain it after successfully stopping the train during the Huge Materia quest.