Surprisingly straight forward and simple once I remembered the much more usefulness of Explosive Gel and Multi-Batarang, been so long since I've played this. Just a little angry they did not release this for PC. Thankfully a coder was able to program it for PC on Steam. I provide a realistic simulation on how to complete this challenge with both speed and no damage taken.
Played on PC [maxed settings] with Xbox 360 Controller.
Final Time: 35.71 seconds.
Bullet Proof - Take down all of the henchmen without taking damage.
Pre-Emptive Strike - Take down the high security henchmen (in red) first.
Three Strikes - Punch any three different armed henchmen
Crouch and spray Explosive Gel behind the henchman in front of you. Run back and perform a running kick
As soon as possible grapple to the gargoyle directly in front and on top of you and wait for the high security henchmen to appear. Throw the Sonic Batarang near him and detonate to get "Pre-Emptive Strike".
The Explosive Gel should automatically detonate by that time since all the other henchmen would have been in that area to investigate.
Simply guide down and Ground Takedown + Strikes to get the remaining "Three Strikes". Remember to quickfire Batarang while in a combo to quickly down any henchmen that are about to shoot you. Doing that will allow for "Bullet Proof".
Hope this is useful in getting your challenge complete!