Jump to grab the handhold on the pillar and traverse around the corner. Be aware of the giant spider that may lurk below. It may appear a bit later, so stay sharp. Release to grab the corner of the handhold below and climb a bit to the right.

Release to grab the narrow ledge below and pull up to hug the wall. Jump to the left (Lara's right arm) to grab the handhold of the next pillar and drop to the beam below. Turn around and shoot the giant spider that crawls the side of the next pillar.

When the spider falls down, walk to the other side of the beam. Jump to grab the narrow ledge on the pillar and traverse to the left to reach the opposite side.

Drop to the beam below and walk to the other side.

Jump to the small square ledge ahead, then jump to grab the narrow ledge on the pillar ahead.

... to land on top of the short pillar. Turn right and and jump to grab the walkway. Pull up.