This level has something like checkers made from crumbling tiles and normal tiles running along the sides of the tunnel. The thing with this means that they are all connected diagonally, meaning that stepping on one dislodges an entire chain of crumbling tiles. The overall strategy to getting this achievement is avoiding the tiles, unless necessary.
The Child is probably your best bet in terms of character. His low weight does not cause the crumbling tiles to dislodge beneath him. Walk across everything as if they were all normal tiles without jumping and you can complete this without jumping at all.
The Skater also works on this Infinite Mode level. The Skater's speed will let you breeze through the crumbling tiles, although the ride may be bumpy.
The Pastafarian using its light bridge really helps when you dislodge the tiles and walk on the bridge where they were. It also helps when there are large gaps between normal tiles.
- This achievement used to be called Falling Gray Stuff Ahead. It is unknown why the name changed.