Once you have the hack tool just go up the stairs they come down (before they come down) hide behind the box and right against the wall so they go past you then just sneak past the last guy at the far end of the walk way (by the objective door). Wait a bit and he'll turn around and go into the loungy room that is up the little steps. It's a straight shot to the door. Just be sure to crouch and not walk or run.
(I was playing on medium when I did this)
This worked, thanks.
I really hope this game improves, like you all claim, or I think I'll die of a broken heart.
[edit] What in the actual fuck. I LOCKED THE DOOR BEHIND ME to stop them from following, but I guess because it's a scripted event they can open it and follow me? That's lame as fucking hell.