After you climb up the craggy surface and stealth kill the two men with their backs turned, create a rope bridge right in front of you. Climb over the gap and head up the stairs.

Look for the white symbols and you will see a cave in the cliff wall. Enter and light your torch. Walk down the path and you will find the Hall of Ascension camp. Push past the strong wind that blows across the bridge and enter the building.

Wind gushes out of the shutters to the left. Move past the wind and use your axe to crank the shutters shut. Run back over to the platform that hangs an inch off the ground. Stand by the crank and wait until the bottom shutter opens. Then start cranking the platform up. Climb up on the structure and jump to the platform. Wait for the rest of the shutters to open so you can be blown over to the wall. Scramble up the wall and follow the ledges to the balcony.

Walk to the back of the entrance to find a chest with your reward. Exit the building and upgrade at the camp. Leave the same way as you came in.

Tomb of the Unworthy Hall of Ascension Well of Tears
Tomb Raider (2013) Challenge Tombs

Tomb of the Lost Adventurer DLC · Tomb of the Unworthy · Halls of Ascension · Well of Tears · Chamber of Judgement · Stormguard Sanctum · The Flooded Vault · Temple of the Handmaidens