Barret's ultimate weapon is a gun called the Missing Score. It can be found when you return to Midgar to try and stop Hojo. You will find it on a landing on the stairs that lead to the Sister Ray. However, it will only be there if Barret is in your party.

Barret's Level 4 Limit Break

Catastrophe, Barret's Level 4 Limit Break, is found in North Corel. After you save the town from the runaway train, walk into a tent on the left side of Corel and talk to a lady in there. She will give you Catastrophe. If you can't find the right tent, just walk into every tent and talk to all of the villagers. You'll find it eventually