Note: This achievement only appears when you have brought the Duplicator.
There isn't much of a strategy to this. One tip is to just normally run in Infinite Mode using the Duplicator without concentrating on having duplicates fall. Another way is by going behind a box and have the Duplicator spawn duplicates, and move to the sides. This way, if a duplicate is spawned and you move left, it will go further if it's not behind the box, thus, eventually falling and giving you progress on the achievement.
The name is most likely a reference to the song "Falling to Pieces".