Although my soloution is similar to Yoo911619, i did it in a different order becuase their solution didnt work for me.
Tips - You have about 5 seconds after eliminating a henchman to get out before the Joker notify's the henchman that one is taken out, so move quickly.
First Predator Mission:
Leave the henchman at the destroyable wall till last, i tried going for him before and he just kept turning round and looking at me so then spoiled the achievement.
Henchman 1. Run and take out the henchman at the staircase, after that i went into the vent type area on the staircase, from their you can pick off the 3 that come next.
Henchman 2. when the 3 come running, 2 will normally split off, to cover each other and 1 will stay near that area or start heading up the stairs, take him out and hide again.
Henchman 3.Sometimes the 2 will split off at this point, other times they stay together.
Split-Same as above.
Stay-If they stay together then go through the vent in your hiding area, then below ground level to the other end of the room, by then they will have split up. and you can hide back in the maintenence entrance.
Henchman 4. the guard you didnt take out will normally investigate the last henchman by himself, leaving him vulnerable.
Henchman 5. (Wall): IMO this is the hardest one because he only moves from the wall when he is last that is conscious. so you can take him out easily.
I Did it in this order because as stated above, the wall henchman kept catching me.
Might post a video at a later date becuase it looks hard to understand the way i have written it.
EDIT : Neg voters :l... why?