While both these solutions are good, I'm going to add something that I didn't find suitable for a comment. Please don't downvote it, I'm trying to help you out solely.
Once you destroy both blimps the achievement should pop. If it didn't, let yourself die or reload the last checkpoint since it should have you coming out of the elevator. If that doesn't work after multiple attempts, turn on and off your xbox and then continue the storyline again. If that doesn't work, install the game to your harddrive and then attempt again.
There seems to be some buggy issues with this achievement, and I myself had it take four tries before I got it. Hope this helps anyone that is thinking about taking this one on.
Also: the achievement is for blowing up both blimps before you get on the blimp on Act 3, Leviathan. When you get out of the elevator look to your right. There will be two blimps with people firing at you from them. Simply stay back and fire inbetween the holes of the grates to take them out. Two shots will take each one down. Sometimes they don't disappear from the screen right away - there's a slowdown lag time. Do not panic and shoot a thousand shots at each.
Hope this helps.