run straight into the room after the video, back straight out and over the edge run around get more health and killing blk hands, run back into the room and into one of the cages(i chose the one on the left)
stay in there, kill any blk hands you see from the room pull out your personal ion cannon if you still have it if not, choose your most powerfull weapon and wait for petrova to pop into view. shoot her and wait for her to come back, keep shooting her till she is dead, then save
then do not pick up the secure card until you have run around and killed remaining blk hands and collect all armor, health etc. then go back to the room and save
pick up secure card then leave sydney in the room as you go across the way into the red doors and kill all blk hands in there and in lab below, then go back and get sydney go back to the red room across the way and down to the lab go into the core(red doors in the lab) kill all blk hands in there and any you can see above you. join sydney on elevator go up. kill all on that level and try to shoot those above you keep repeating this process all the way up, save often if you have good health and always shoot those above you till you get to the top. watch the rope that the blk hands keep coming down once you get to the top, protect sydney as she hacks the computer and you are done