The tile are not all connected, so use the Runner to move sideways quickly and destroy the crumbling tiles. The Runner can move sideways over one-tile gaps.
The Lizard is also a good choice because it has a low speed, so you also have more time.
The Duplicator is also a good choice because his duplicates can crumble the tiles also, but he costs a lot of power cells.
The Child is not a good choice because you have to jump to make the tiles fall. On top of this, the Child's jumps are so lengthy that this may make earning the achievement even harder.