You can beat this with the Pastafarian by using her light bridge to your advantage. You just move left or right. (Note: Only for normal tiles. She stinks with crumbling tiles.)
The Duplicator is also compatible with this achievement as his duplicates can survive if you plummet into the void.
The Lizard's slow speed and high maneuverability can help you succeed with this achievement.
For laughs and giggles, you can achieve this with the Gentleman without actually doing the achievement in the intended way. Jump before entering the level, then use power cells to glide across the whole thing. You will still get the achievement.
Note that if you bought the box upgrade, you can stop yourself, compose your thoughts, and well, achieve this achievement with almost any character.