If you aren't interested in achievements/trophies, or already have them, you can take the less stressful route described here.
Step forward to trigger the cutscene: The door closes behind Lara, and molten metal flows in, triggering a series of eruptions.
Stand near the entrance and wait for the molten metal to trickle down to the pool of oil, igniting a wall of flame that rolls across the pool. After this, there will still be random eruptions, but things will be a little calmer.
Quick-save if you like. Then move down the slope, avoiding the pits and rising blocks (marked with X's in the screenshot above).
Walk out to the end of the central cluster of hexagonal blocks, some of which sink into the pool behind you.
Take a standing jump to the next cluster of blocks. Be sure to land on one of the ones directly ahead...
...since the middle-left block rockets upward when you get close.
Walk forward and take another standing jump onto the left block in the group of two directly ahead (i.e., the one that's slightly lighter in color than the others).
Turn slightly left and take another standing jump onto the farthest of the three blocks ahead. (The nearest one is another rocket block.) Then take another standing jump onto the nearest block in the cluster ahead on the right.
From here, you can either take a curved running jump to land on the staircase, or walk forward onto the block nearest the stairs and take a standing jump from there.
Climb the stairs and claim the FIRE CRYSTAL (1).
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