The first thing you need is the "Wall Fly" skill. You get this quite a bit after you can access the Proving Grounds area for the first time so progress through the main game until you have that before attempting this. You'll ideally have a fair bit of stamina by then too which you'll need. You do a Wall Fly attached to a wall and the Y + the direction away from the wall.
This is the second challenge (from the left) on the bottom tier of the proving grounds.
There are 30 exploders so there is a little leeway. The achievement pops before completing the challenge, just the moment you get 20 during the challenge. I it is NOT cumulative and has to be done in one attempt.
The suggested approach would be to get this out the way as soon as possible of the 30 exploders as the level is easier at the start. The platforms and the walls disappear and reappear but you can launch off of them as they are disappearing for a second or so. You can also leap out of your wall fly if your jump to the other side doesn't have a platform. This is important to do if there won't be one as you'll slide to the bottom and die and have to restart.
Final tip, I'd get the 1st 10 or so successful wall fly kills guaranteed but when you feel you're getting close focus on staying alive and killing the exploders in time and you should hopefully get it after a few attempts. My successful attempt I ended up doing an upper cut or two in the middle before finishing the run.