Mate it took me quite a few attempts too. In fact, I've been playing through on easy and so far everything has been straight forward.
One thing I found is that the moment she starts on the first computer, run up the left stairs and stay at the top - you can take out the guards as they come running, and only a few come from the right hand stairs.
Then just before she finishes (can't see any more guards) run back down the stairs and I tend to find a guard has dropped a much better gun with a decent reflex sight. First few times I played I never got that gun.
2nd computer take out as many guards as you can as they run through the door, and watch out for a guard who comes in behind you on the left. Reflex sight makes taking out guards through the smoke fairly easy.
You have to watch out for a handful of guards with grenades coming from the right - perhaps more stuff was blowing because of them.
But yeah, hardest part of the campaigns so far for me