In the previous section, Lara entered this room and killed a hazmat-suited guard (12), while avoiding the Leviathan in the pool below. The exit is on the far side of the room. In order to climb over there, you'll need to shut off the steam venting from one of the pipes along the right wall. The valve that does this is on the larger pipe along the opposite wall.
So descend to the metal platform just above the surface of the pool. Carefully jump out onto the pipe and activate Walk so Lara doesn't fall off. Pick up the Mag Vega clip (11) and turn the valve.
Walk back along the pipe and jump over to the ledge.
The achievement/trophy "Into the Hellmouth" requires you to "swan dive into the Leviathan's reservoir." There's no need to dive from any great height, so this is a perfect spot. Aim for the pool, start walking forward...
...then press Jump to swan dive.
The achievement/trophy should pop when Lara hits the water. (If you miss this opportunity, you can try again the AQUATIC RESEARCH AREA.)
Climb out of the water using the either ladder.
Now head for the vine-covered corner below and to the left of the entrance from the steamy passageway.
Face the wall to the right of the corner.
Jump up and grab the vines. Then climb upward, right, and up some more...
...to reach the ledge above.
The door ahead doesn't open. So climb the ladder to the high walkway...
...and use the switch...
...to move a small platform toward the far end of the room.
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