When Lara slides almost to the end of the slope, jump forward to grab the handhold of the square pillar before you fall into the chasm.

Traverse to the right around the corner, but do it quickly because the handhold is about to collapse.

Jump to grab the handhold on the next pillar and take a breather if you want, since this handhold is stable. When you are ready, release to grab the horizontal pole below.

The pole is about to fall, so traverse to the other side and release to land on the slope.

When you reach the end, jump to land on the beam ahead. The beam is stable, so take your time. Walk to the other side of the beam.

Drop to the next beam at other side of the pillar. As you walk on the beam, you will see a giant spider crawling the side of the next pillar. Shoot it and it will fall down.

This beam does not reach the next pillar, so jump the gap to grab the narrow ledge there. Traverse to the right around the two corners until you reach the broken part of the ledge.

Pull up to hug the wall and jump to the right (Lara's left arm) to grab the other part of the ledge. Traverse around the next corner and pull up.

There is a beam exactly below, but do not go there. Instead, perform the Chimney Jump to grab the edge of the safe walkway above. Then pull up.