Once in the Main Chamber, head over to the left. Look ahead, across the massive gap in the floor. You will see some crates against the left-hand wall. Climb up to the platform above them. Use the rope to cross the gap. At the top, jump over to the ledge to the right. Follow that around the corner then drop down. Head forward and go through the doorway in front of you.
Free run across the beams to the far side of the corridor. Head on forward.