As
Rossco7530 and
Dmbledore mention in the Comments section of one of the other solutions, this can be done in private horde.
All you have to do is pick up the fabricator and don't put it down until everyone but the player holding it has pulled the horn and the lever is once again available to be pulled. At that point, the final player puts down the fabricator and pulls the lever. The achievement pops before the enemies begin to spawn.