This achievement may take some time to figure out how to do if using a character besides the suggested ones, but after you figure it out, it is very easy.
Basically, when you start the level, you have to move right until you are right next to the side that's to the right of where you start. In that thin area, one of the sides will always be there for you to stand on, so you will complete the achievement.
Any character will work, but a cheap and fast way is the Skater, as he is probably your fastest way of getting this achievement, since his high speed lets him glide past those alternating gaps with more ease than other characters.
The Pastafarian on the other hand makes this so much easier as her light bridge will not require you to go to the edge of the tunnel and instead just catch you wherever you fall. However, buying her just for the sake of the achievement is not worth it as she costs 60 times more than the reward of this achievement. You won't unlock Skater until Level 10, so play through level 10, then go back to earn this achievement.
The Bunny can also earn the achievement easily, because it can jump without you pressing anything, which is very useful.