The Lost City - Climbing to the Third Trebuchet

After taking out the 2 archers protecting the third trebuchet...

Use a rope arrow to create a zip line from the lower deck of the second trebuchet to the tower below and to the right (east). Slide down and then climb onto the upper ledge of the tower to find some magnesite.

Use another rope arrow to spin the long, horizontal beam so one end points toward you.

Jump onto the beam, walk to the far end, and jump from there to the ice wall ahead. Climb to the handhold above.

Then climb around to the left until you can jump and grab the horizontal beam jutting out of the tower.

Pull up onto the beam, adjust your position if necessary, and then jump forward to grab the handle of the dangling golden bucket.

The bucket swings around to face in the opposite direction. When it settles, climb/jump straight up onto the beam above.

Jump to grab the wooden beam ahead, and then climb up onto the deck.

You won't have to deal with the Deathless archers if you killed them earlier, as shown above, but a swordsman and a heavy soldier with a polearm attack immediately. If you act fast, you can shoot the Greek fire vessel to take out the swordsman as he charges.

Then either take cover on the right and fire at the heavy soldier as he approaches...

...or move forward to meet him and use the Dodge Counter/Kill maneuver. After this, the coast is clear for a while.