|N version||1.4 and later|
Method 1 (Easy/cautious)
Drop down and activate the thwump, then ride the thwump upwards. Two guided zap drones will be heading downwards (one will have already seen you); do not worry, as neither will both you. After the thwump stops, jump off to the right side and walljump up. One zap drone will be right above you; let it see you, then quickly jump off to the left onto a bounceblock. The top thwump will activate. This takes a little bit of timing to pull off.
Wait for it to go, then get the exit switch and carefully drop down on the left side. This can become surprisingly frustrating. Luckily, none of the zap drones hug the side wall as long as you don't attract their attention there, so if you can slip down the left wall, stopping between the gaps of the mines, getting to the door becomes easy. Once you make it to the bottom half, hitting the slope to stop your fall, then run to the door (watch out for any trailing drones).