Spacelines from the Far Out

First you need to acquire the mop from the Upgrade store. It will appear at random, so RNG plays a role here. Alternatively, the mop is part of the starting loadout for the Model 500 and the Svetlana.

You could wait for this to unlock through natural progression but read on if you want it fast. First flip the gravity off by briefly cutting power to it. A few seconds is usually all it takes to make one of the passengers sick. Do not take them to the infirmary, but instead let them be sick. Before cleaning it, bring other passengers to it and stand in it yourself to create as many piles of it as you like. Then take the mop and clean them up!

Note: If you do not clean the mop with the bucket before its bar fills, it will leave several messes behind. I did not test if these also count for the achievement.