You only have to slay the Smoke King on each level in order to complete it, however killing every single monster on a level will enable you to get an added bonus.
Once the soot monsters explode, they hurl out more debris - make use of this to your benefit when trying to obvious the entire stage.
When beginning a brand new level, always employ the first couple of tries to experiment. Get a concept of the way the environment affects the movement of the pebbles before mounting any serious challenge.