Do you remember the wooden platform in this room where you killed the spider? You got there using the matal ring above the ledge with the destroyed corner. Make your way again to this wooden platform* and, as before, jump to grab the metal band on the grinding machine.

(*If you do not remember how you reach the wooden platform, refresh your memory by reading this page.)

The next part of the main cylinder above rotates anti-clokwise, so traverse to the left. As before, you will give Lara some time to climb up the next bands.

Wait until you see two metal bands; again, one above the other. Jump up twice to grab them.

Jump up once more to grab the band that does not rotate. Traverse to the right as much as you can, but be careful of the spiked roller.

When you see a band passing above Lara, jump up to grab it. The band rotates to the left, so keep an eye behind you to spot the vertical column.

Jump to grab it. You can time the jump by climbing to the right if you get past the column, pressing the Interact (Y) button at the same time to make Lara move faster. If you pass the column and run out of handhold, do not keep hanging there because the band will rotate and take you to the spiked roller. Instead, release to grab the band that does not rotate below and try again.

When you grab the pillar, a giant spider appears below, so shoot it with one hand. Otherwise, jump to the opposite wooden ledge and kill it from there.