The objective is quite simple: you have to kill all the enemies in every stage. There are 20 enemies per stage and there is 4 different kinds of enemies (see "IV- About the enemies"). You can only move to the next stage only if all 20 enemies have been eliminated.
The game is over when all players run out of tanks OR if anybody shoots at the eagle (or whatever it is) located at the bottom of the screen. So, your mission consists not only about shooting everywhere, you have to keep an eye on that bird. And remember, anybody may kill the eagle, even you.