First of all let it be known this is the only part of the game I have found difficult.
This fight seems to be inconsistent as one time 1 of the 5 enemies with Deadshot just magically vanished so I was able to do inverted takedowns on all 4 then go to town on him. He takes a hostage and I dont stop him in time so no big deal I start over. Only problem is TWO TIMES IN A ROW NOW. He IMMEDIATELY executes the hostage. This has to be some kind of glitch? I have no idea how I am supposed to prevent that because once you beat him down to the point he gets the hostage the room fills up again with armed enemies sometimes even with a jammer making it even more difficult. He literally just suddenly seems to be immune to stun and runs rigth at the hostage and kills him right away.
Take out the jammer guy first, then don't worry about other baddies. Just focus on Deadshot. As long as you don't beat up the rest of this guys, then no more jammer guys will come in. --- "I've been diddled again!" --- Plok
I did this about an hour or so. Best case for what I did is when we takes the hostage make sure you go directly for the vents. Be in the vent and get the timing down for the final patrol. I didn't take the time to take them out so I over complicated it. Then just watch him spin around.