This is the tough speed run out of the three. The video will show you the route which is the first thing you need to memorise. It seems like rolling along paths and jumping down stairs speeds things up a bit.
The combat is the make or break section as skipping it will leave Elena getting killed. You need to take out the first two ASAP and then get a .44 revolver off the first two enemies you meet so you can take out the rest with one shot.
There is a last shotgun guy just before the ladders and I found it best to run past him and then turn and kill him. If you ignore him he will likely kill you.