During the Backseat Driver chapter, commandeer either Banshee that the Elites give you on the platform. Destroy the three Wraiths that Johnson's Scarab is targeting, and make sure that the Scarab will start moving after the tanks are destroyed. If it does not proceed, check the area and eliminate any additional enemies that you may have missed.
When the Scarab starts moving, land on it and wait until it reaches the middle of the canyon, with the huge rocks in the center. While you wait, note how your entire Banshee swings back and forth as the Scarab walks around. Jump off the Scarab, and make sure you land on a slope of the rock in the middle of the canyon, so that you survive the fall.
The game will still think that you are on top of the Scarab, even though you are on the canyon floor. This is because the developers did not expect players to survive the fall from the Scarab. As a result, you will continue to sway and swing around as if you were still on the Scarab. Unfortunately, though, you will have little control over your movements in this state.
After you are on the canyon floor, your survival is not guaranteed, for Brute-controlled Ghosts and Spectres will attack you, while you have little control of the Arbiter in his "swinging mode." If you wish to exit the "swinging mode," you should revert to the last checkpoint, because committing suicide with grenades is futile—you may not even hit yourself with a grenade in this state.