In the southwest corner of the cave, opposite the sphinx's left paw, is a light-colored block just the right height for climbing. Get on top of that block then take a standing jump to the angled block to the right. Turn around and take another standing jump to grab the brownish ledge above. Pull up.
Walk along the ledge to get the magnum clips ahead on the left.
Then turn around and make your way back along that same ledge to the spot where you just pulled up. Vault onto the low ledge to the left and then jump the gap to the ledge ahead (the one with a low sandy step above it). From there, take a running jump to the next higher ledge.
Turn left to face the cave wall. Climb onto the ledge ahead and above, then to the block on the right, where you'll find more magnum clips.
Now turn so the cave wall is on Lara's right. Climb or jump onto the angled block ahead. Then jump the gap to land on the next flat block. Do the same again and continue down and to the left to the switch.