As with all the bosses in this game, you only need to do 1 thing: TYPHOON!
Seriously though, max out your typhoon as soon as you can. On "Give Me Deus Ex" difficulty, you can drop this guy, and the other bosses as well, with 3 typhoon hits.
All you need prior to any boss fight is:
1.) Maxed out Typhoon
2.) Typhoon ammo
3.) Energy bars
Barret is at the end of the FEMA mission.EDIT:
Wow, I see people haven't changed: handing out a negative vote without letting me know what is wrong with the actual solution...
I guess some people want you to hold their hand throughout the entire process