For the Bluntnose and Hopper, you need to get out of bounds without boosts. The wall behind the starting position is short enough for vehicles to climb it with normal Wall Climbing.

Use Boosted Wall Climbing to scale the tower. You will need to extend the climb by spamming brake. 

Once in the air, use your other two boosts and tap the breaks repeatedly to alternate between boosting forward and boosting upward. During the moments where you're breaking, align yourself with the left strip of the pit; everywhere else is a death zone. 

Hug the left wall on landing, as the right side is solid and will cause you to crash. Jump just before you reach the end of the ledge to clip back in bounds. 

The Vector and Cruiser requires much less setup, as a single Boosted Wall Climb can scale the wall much quicker than the other vehicles. 

3 Vector Boosts or 2 Cruiser Boosts can cross the pit without needing to climb the tower. Aligning yourself with the landing stip is much more important when coming into it at an angle.