The objective of Super HyberDoze is to destroy the bad dreams before they wake the girl up.
Bubble: Click a bubble to pop it. Cloud: Click a cloud and shake it back and forth to destroy it. Flame: Drag it to make sure it's not over the girl, then click it repeatedly to put it out. Rock: Click and drag it, move it quickly toward the ground, and release to throw it into the ground. You may have to do it more than once.
When destroying a rock or flame, make sure it doesn't land on the girl. The girl's thought bubble will tell you what enemy will appear next so you can prepare for it.