After pulling the switch and waiting for the cut scene to finish, run to the opposite side the ledge. Keep running as you veer to the right, jump off the ledge and grab the left side of the long, broken ledge in the middle of the room. Pull up, grab the lower handhold on the square pillar ahead then jump to grab the higher handhold.
Climb around to the right and jump backward across the gap to grab the top of the broken square pillar behind.
Climb all the way around to the other side and jump backward again to grab a handhold on the next square pillar, which has an angled top.
Climb around to the right and then jump up to grab the top of the angled pillar. Climb then jump to the right to grab the horizontal stone handhold on the wall. (It's just above the round dart pipe.)
Climb to the right, jump and grab the horizontal pole.
Swing and jump to the long ledge ahead. You don't actually need to swing all the way around the pole. It's quicker to just grab it and then press Jump again to leap off the pole before Lara swings all the way around it.
When you land on the ledge, CHECKPOINT 6 registers. If you've made it this far without too much hesitation, turn right and run along the ledge toward the far corner.
IMPORTANT: If Lara dies during the second phase of the run, the game will reload at CHECKPOINT 6; however, the pole above will have retracted into the wall. If this happens, just hang from the edge of the long ledge with the checkpoint and drop to land on the ledge with the switch. Then you can pull it and try again. If you reach CHECKPOINT 6 and you feel you've taken too much time, you can save the game manually, reload and drop down to the switch to try again, as shown in the screenshot below.
[Part 2 | Return to the Walkthrough]