The ghost can't harm Lara (much) while she's crouching, so immediately duck and start crawling around for the pick-ups. You'll find a large medipak, 2 boxes of V-Packer shells and the V-PACKER SHOTGUN (if you don't already have it) along one edge of the room and 2 more boxes of shells on the other side.
Now figure out which of the standing statues has the blue light. Crawl toward it but don't get too close or the painting will move to a different statue. Once you're in position, save your game. When the ghost moves away, stand up, draw the shotgun and crouch down again. (Here is a screenshot of Lara in the spot that worked for me.)
Shoot at the ghost when it swoops toward you. Don't bother to turn around, just wait for it to come back for another pass, and then shoot some more. Eventually it will be stunned. If you get lucky, it will stop behind Lara. It only pauses for a few seconds, so quickly holster your gun (otherwise Lara can't run straight) and run toward the statue. As soon as you see the Hand icon, press Action to grab the painting. Then crouch again.
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