The achievement might be broken when playing on a different language setting than english (possibly due to the level categories being named differently). It didn't count progress and didn't award achievement when playing in german. When I switched to english and replayed medium level 20, I instantly got the achievement.
Note: You don't have to jump to get up. You put the mouse directly beneath your character and then draw up to push your character upwards. Very useful for multiple levels that are about dodging.
Great game. Challenging but rewarding and not (too) frustrating due to well placed safepoints. And I love the "no jumping" mechanic as it makes it more of a puzzle and timing and less of a "pixel perfect execution" game.
Except for the expert level. That one is a all of it at once. Still great though :D