The object of Cosmic Crisis is to defeat all of the enemies of each stage thereby advancing to the next, harder stage.
To do this you'll need to dig holes in the green levels by holding down the "x" button. Next you'll have to lure the enemies into your holes and fill them up quickly by holding down the "z" button. If you're not quick enough the enemies will escape!
As you progress into harder levels you'll encounter harder enemies that will need to be dropped through more consecutive layers.