Head over to the right of the big wooden bridge in the Summit Forest. There will be a cave with a source of fire next to it. Enter the tunnel and follow the passage until you reach the main room.
Light up the burner that hangs towards the camp for a little light. Burn away the debris that sit up on the platform in the green gas with a fire arrow. Then blow up the gas with another fire arrow and scramble up the wall. Run to the left and scramble up another wall before the gas comes back and chokes Lara.
Hit the Survival Instincts button to have some debris blocking the craggy wall glow. Burn it with, yet again, a fire arrow and then balance your way across the beam. Jump at the end. Attach your axe to the wall and climb up. Open the chest and claim your reward. Carefully make your way back down to the ground and exit the cave.
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Tomb Raider (2013) Challenge Tombs