Serial Cleaners

Perfect cleaning means basically getting rid of all blood on every single level, even if this is not the objective of the mission. You can die as many times as you want but make sure to clean that blood.
The tutorial does not count towards the achievement.
Once you get rid of all the blood there's going to be an animation at bottom of the screen indicating you're good. It kinda looks like Mr. Proper from commercials. Until you see this animation keep cleaning.

Another super important thing to keep in mind. There's no mission select in the game so it's better to aim for perfect cleaning in the first playthrough otherwise you sign up for another. Good thing is that achievement works cross-save. I didn't get 100% on level 1 and after finishing the game I started a new playthrough on a new save and upon completing the first mission achievement popped.