The basic plot of the game is "Oh no, the evil overlord stole the galaxy crystal, we must fly up to the moon to get it!" In more concrete terms - first few levels are in a jungle. The next 3 levels are flying up an exploding volcano. The last 3 levels are going to be on the moon. And of course, there is a big boss ;)
After shooting the enemies they will become airbubbles. Jump on those bubbles and let you transport to higher levels.