Jump on the large rock in the pit below. This will roll as we jump on it. As such, we can use it to traverse to the other side of the spike pit. Try to stay just on the right hand side of the boulder to keep it moving and continue to jump towards the left, where we came from to prevent our silhouetted hero from falling down.
As you cross the gap, you will see the spider re-appear on the ceiling, so be ready to jump from the rolling stone to the far ledge as soon as you are able.
Slide down the hill and continue to the right. You will see a dead body, walk towards it and the ground will give way. Ahead you will see a rope with a trap attached to it. In order to use this, jump to the rope, and then quickly jump off the rope. This will dislodge the trap and allow you to use the rope safely.
Use the rope to swing up to the ledge on the right and keep on moving.