It IS possible to kill the large alien ship. You must shoot it in quick bursts, keeping your laser energy high, and you must keep shooting it when it moves backwards and off the screen (you can barely make out the lights on it).
Another thing that you have to do is when you come up on the paddle boat just before the balloons, (I think that's where it is) quickly empty your laser energy onto the red paddle. Depending on how good a shot you are, you should rack up about 200 to 300 points.
Another trick to get points is to shoot the yellow boulder on top of the canyon in the desert area. It is kind of tricky to find, and took me a long time to find it. When you enter the desert area, pay attention to the top of canyon wall on the left side . You will see a hexagonal and a pyramid shaped boulder, and in between them you will see an odd shaped yellow one. If you can shoot it you will get a quick 200 points. If you are a good shot and have quick reflexes you should have about 4400 points when you get to the large ship.
Here is one final trick to get some good points, if you need them. At the end of the course, when you are about to finish, there is a row of lights on the left side. If you aim your crosshairs at the lights and start firing in quick bursts to keep your energy up, and you hit the last one, you will get 200 ponits.
If you really, REALLY, want to win this mini-game, go out and by a TurboPad. This gives you infinite energy, and makes killing the Alien Saucer very easy. Doing this is cheating, however, and I don't endorse that kind of thing.