without grapple swing: ruined shrine
Shoot the gel crystal to bring down the first bridge and grapple point. When it stops, space jump right at the golem's arm. You should make it with no problem, as it's unusually easy to push up onto. Jump again to get on the bridge itself, then get a running start and space jump to the ledge above. It might look like it wouldn't be reachable from here, but it is; try approaching it from the side, going between it and the branch next to it.
After you land, there's another gel crystal by the wall. Shoot it and continue up the room, shooting a third gel crystal. The last bridge will come down, leading to Hangar Bay.