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You can't kill the Keeper, but you can stun him using your shotgun. Its best to do this fairly near to the statue holding the painting. When you have shot him until he is keeping still, holster your gun and run to the statue. Press that action button to grab the painting. After that you need to run for the exit (perhaps stopping to pick up all the ammo and health littered about the place), where the corridor is now flooded with water, and the keeper can't follow you.
Hmm
No im not going to tell you. Obviously