In order to get Barret's final limit break, you need to unlock the six prior limit breaks and obtain the item that teaches Barret his final limit break. The way to unlock each limit break differs for each character but are essentially similar. You unlock the second limit of each stage by using the first limit of that stage a bunch of times, and you unlock the next stage by getting a certain number of kills.
Barret's limit breaks:
Stage 1: Big Shot, Mindblow
Stage 2: Grenade Bomb, Hammer Blow
Stage 3: Satellite Beam, Ungermax
Stage 4: Catastrophe
Unlock order:
Use Big Shot 9 times in order to unlock Mindblow.
Get 80 kills with Barret in order to unlock Grenade Bomb
Use Grenade Bomb 8 times in order to unlock Hammer Blow.
Get 80 kills with Barret after unlocking Grenade Bomb in order to unlock Satellite Beam.
Use Satellite Beam 6 times in order to unlock Ungermax.
Use the Catastophe item after unlocking previous 6 limit breaks in order to unlock Catastophe.
The Catastrophe item can be found in North Coral, but only after completing the Huge Materia quest. Talk to the woman in the ruined building near the Inn and she will give you the item.