You need to destroy all of the rocks in one stage, so use the driller's class with improved mining speed. I did it on salt pits with the idea that the enemies would help destroy terrain which worked reasonably well. I focused on mining and move speed upgrades, and got it on stage 5 well before the boss spawned.
Using plasma turrets with the wall-destroying overclock is also a good option. I'd use a tinker engineer for that.