Having the passage with the Large Medipack to the back of you, you should be able to see a pillar on either side. The left one is taller, but there is a slope in front of it that will help you grab the pillar. Jump up and grab its edge. There is a second taller pillar right behind you. To avoid inadvertently hitting it and messing things up, shimmy to the left-hand corner of the pillar you are hanging from, and tap the right direction key ONCE.

Pull up and back flip to the second, taller pillar behind you. Do not let go of Jump. Once you land on the second pillar, you will jump towards a third (even taller) pillar. Still holding the Jump button, press Action and you will jump again to grab the right hand part of a fourth pillar in front of you. (Warning: This particular jump is very tricky. You have to position Lara very carefully from the start, so she can grab the pillar.)

Pull up and you will start sliding. Do not let go of the Jump button. Its natural angle leads you back to the crevice. Press Action to grab its edge.