Tomb Raider Pyromaniac Challenge objective: Shoot five Lanterns in the Mountain Temple.
Use the ladders to climb on a wooden scrabble wall. In the ruined Temple you can find the first Pyromaniac Lantern.
The second Pyromaniac Lantern is above the base camp, hanging from the roof edge of the Temple.
Go up the stairs from the base camp, and defeat two enemies on your way. Check out behind the building where you have spotted the enemies.
During the mission you will enter one of the temple house. Destroy the Pyromaniac Lantern in order to proceed with the mission.
Use the Zipline to leave the burning temple. Go slightly backward, and take the left path which leads you to the building where you can find the last Pyromaniac Lantern, hanging from the roof edge.