Run into the room and kill the baton-wielding MP...
...before he goes down the hall to the right and uses the handprint scanner.
This activates a set of laser tripwires connected to the gun turret in the main room and alerts another soldier, who emerges from the hallway on the left (i.e., directly opposite the hallway with the scanner).
NOTE: If the MP manages to activate the lasers, I suggest reloading your last save and trying again, since the lasers and gun will make the next sequence much more difficult. If you insist on getting all the kills, let the MP go. Then after he's armed the lasers, kill him and the soldier, and shoot the gun turret so it won't go off when you touch the lasers.
Climb onto the bank of computers in the middle of the room, move to either end, and jump to grab the edge of the catwalk on the side wall. Press the button to call in a soldier.
Then drop down and eliminate him. Note that the soldier does not come through the door you open with the button; he appears in the hallway below the catwalk. As long as the laser tripwires haven't been activated (or you destroyed the gun turret), you can run and jump around all you like as you fight. If you haven't destroyed the turret, take care that you don't hit it by accident or it will start shooting.
Repeat this process with the catwalk and button on the other side of the room.
Again, the soldier comes out of the hallway below the catwalk, not through the doors that open when you press the button.
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