Tomb Raider I-III Remastered Starring Lara Croft

https://www.xbox.com/play/media/eNC3idtuZZ hope it helps

This achievement takes place in the Offshore Rig level in TR2. At around half a level, just after the dormitory room where you can get the automatic guns and harpoon gun, you will arrive in in a room with four burners and two ladders, one of which you arrive from.

The normal way to get out of this room is to pull two blocks and jump above the fires, grabbing the ladder just beyond. For this achievement though, you can't grab the blocks at all, so you will need to walk or run exactly between the four burners, reach the wall, then do a side step to the right and grab the ladder. If you walk perfectly in the middle of the burners, you will not catch fire, but you will still take a lot of damage, so use medpacks to stay alive!

The achievement should unlock in the corridor right after the top of the ladder.

Tomb Raider II - Offshore Rig (Level 5)

After climbing out of the trapdoor in the bunk room, go to the end of the passage and slide backwards down the slope to grab the ledge. You can then drop/grab repeatedly down the ladder. Position yourself lined up roughly in the middle of the 4 burners, against the wall with the movable blocks.

Walk forward 2 steps from the wall then perform a running jump over the burners, angling yourself slightly to the right in the air towards the ladder on the opposite wall. Quickly climb up and you should only take 15-20% of your health bar in the process. Climb up at the top for the achievement.

Video:

If you prefer visuals^