Note that there's serious lag when earning achievements. You'll also get the achievement Catlike Reflexes doing this, but the lag may cause you to miss the door.
As soon as the stage starts, jump, press
, then while near the floating platform, press
. You should fly over the swing and start sliding. Start mashing
to open the door! As long as you open the door, it doesn't matter if you slide facefirst into circular saws, you'll unlock the achievement.