Note: Only the Pastafarian can do this achievement.
With the new and improved Pastafarian, this achievement is actually pretty easy. What you need to do is jump at the beginning when you are on a bridge tile. If this is your only time you strengthen the bridge, you are going to have a hard time completing this achievement. However, if you run sideways fast enough and hit a bridge tile, it actually counts to reinforce the bridge. Doing this again and again will easily make enough bridge tiles to carry you to the end of the level without the bridge falling apart and disappearing.