Wacth the guards to see their patrol routes, then time your runs so that you run past when they're not looking. if you cast sprint, it'll help a lot.
Stay well clear of any berserked enemies.
Slowly make your way to the far corner (go around the central path, not along it, there are too many enemies on it). Then when you get near the entrance, just make a break for it, and run straight for the doorway, trying to avoid the guards.
If you fail, just try again. It took me 5 or 6 tries.