Climb Monk Temple tower was a mission in Jak 3. With the use of his new Dune Hopper Jak could jump over the few islands leading to the Monk Temple, arriving there he decided to try and climb to the top.
You'll start at an old cloth which you can use as a trampoline. Do so and grab the nearby platform, where after you must climb higher and higher to the very top of the Temple. It's only a lot of platform jumping and pole swinging, with several of the platforms collapsing when you stand on them, although these are all visibly cracked and easy to spot.