I was hoping that with the "modified boss battles" tagline that the Director's cut would be a bit more challenging than the original. I was wrong.
As with the original 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.
Questions, corrections, and neg vote justifications below.