Just so everyone is aware - on Give Me Deus Ex Difficulty, FOR ANY BOSS FIGHT: 3 to 4 Typhoon hits will end the fight.
Stock up on Typhoon ammo and energy bars. At the beginning of the Barret fight, or whoever, make sure you have enough typhoon shots, and energy bars, to pull off 4 (it may be 3, I forget) and he will go down.
Fight done in under 30 seconds.
And don't worry if he is shooting you - you are invincible during the typhoon animation.
Questions, corrections and neg vote justifications below.