This achievement is very easy with the Pastafarian. Right when you spawn into the level turn right. If you go left your bridge will fail and and you will either have to touch a box or restart. If you move too slow toward the right, you will touch a box. So quickly move onto your bridge and then jump to land on normal tile platform. Your bridge will be destroyed but it is not needed anymore. The Pastafarian can easily jump over the boxes so you can easily jump your way to the end.
If you don't have the Pastafarian, you can use the Lizard. The Lizard would be helpful since it jumps high, but its speed is slower than most characters. At the start, do a big leap rightwards, then make small jumps over the boxes once you land on the platform to the right.
This achievement was originally suggested by Random Pro.