At the start, walljump twice up the right hand wall, and push off to land onto the central pillar. Jump off again once you are balanced to activate the exit-opener - but not so quickly that you jump underneath it and miss it - towards the tallest pillar, or alternatively over that and onto the exit.
Alternatively, walljump quickly from the bottom of the right-hand wall, holding left for as much a time as possible, and this should get you pretty much on the central pillar. After that again just jump to the exit-opener and down to the exit. For the speedier method, you can corner-jump off of the tile as you hit it, which should give you more air to hit the exit-opener and land on the exit in one jump.