Hop down onto the flat spot below the right side of the door (left side if you're facing out from the pyramid). This is where Lara is in the screenshot above. Take a diagonal standing jump up to the next flat spot. Kill the giant beetle that flies up at you. Then turn back toward the doorway and climb up two tiers. Now you should be on the tier above the door. Take a standing jump over the slope to the ledge on the right side of the door, where you'll find a small med-pack.

Take a running jump to the ledge on the other side of the door and pick up the REVOLVER. (At this point, the secret registers and the swarm of beetles emerges.)