To access this Challenge Tomb you need the climbing axe. Once you have it, head up the mountain walls above the plane (the one near the wolves' den) and follow the white paintings next to the wooden bridge and the waterfall.

Jump down into the water and follow the passage back into the cave. You will pass the Tomb of the Unworthy camp.

When you move ahead, you will find a big room with a cage on the right holding up a metal platform with a few cocoons hanging from it. Use the ramp to jump to the platform and then over to another platform with a source of fire on it.

Light your torch and hop back to the platform. Burn the cocoons that hang form the platform to lighten the load. Then jump over to the area with the cage. Shove the cage by pressing the melee button. This raises the platform up even higher.

Jump onto the platform and onto the craggy wall. Climb up and follow the short passage back to a chest. Open it to claim your reward. Get back to ground level by riding the zip line back out near the craggy wall. Sit at the camp to upgrade and purchase skills. Exit the cave the way you came.

Tomb of the Lost Adventurer Tomb of the Unworthy Hall of Ascension
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