Climb on the lowest ledge. Take a standing jump to the opposite ledge. Jump and grab the next one. Jump up to grab the ledge above and pull up.
Now take a standing jump to grab the next ledge and pull up. Do the same thing for the next one and turn around.
Jump to grab the ledge above and pull up.
Walk to the front right corner, make one step backwards and jump up to grab the ledge above; pull up.
For the next three ledges, take standing jumps. Turn left and climb in the alcove above. Pull the lever to open the trapdoor at the bottom of the room.