Use the console on LEVEL 4 to call the elevator.
As the elevator rises, jump down onto it.
Run across it, jump through the hole you just made, and then latch onto the climbing wall with your axe.
Climb upward and to the left. Jump past the corner to latch onto the next section of climbable wall.
Continue climbing to the left until you can drop down on the metal ledge with the salvage crate. Get the salvage.
Then use your axe to pry off the third gear.
Instead of jumping back to the climbing wall, drop down off the ledge onto the walkway below and follow it back around to the LEVEL 3 landing.
Jump straight up to grab the ladder above the console.
Climb onto the ledge above and pry off the fourth gear with your axe.
Now that you've removed all four gears, the elevator crashes down to the bottom of the shaft, and you receive a reward of 100 XP.