|N version||1.4 and later|
Jump up to the left corner of the square right above you (to the right). You will trip on the corner and land safely on top of the square, having just squeezed right under the mine. Now quickly jump up+right before the two guided zap drones approach you, and jump again to the up and right as another zap drone passes you from above. Hang onto the side of the square, then walljump off to the square to your left.
From here, you are right next to the exit switch. You can simply run off the side of the square with sufficient speed, and you will touch the exit switch and land on a square to the bottom left (however, if you go too fast, you may crash into the square to the left, and you will die on a mine; a couple of times of experimentation will allow you to adjust your speed). The more cautious way is to just land on the square below the exit switch, then to jump up and grab the switch. However, beware of the zap drones everywhere. Slowly descend and get to the exit.