This Seeking tech guide will explain how you can beat Uber-Foe in Astro Bot. Use the following video as a reference:
For the first step, avoid the dynamite enemies until they explode. You can then use your rocket on the UFO circling around the edge of the battlefield. You may have to get ahead of its path in order to hit the saucer.
Afterwards, avoid the exploding enemies again and then take care of any remaining stragglers. The UFO will move from one side of the area to the other before temporarily stopping and doing the same thing again. Attack the saucer when it reaches the edge.
Next, you need to avoid more dynamite enemies before you take care of any remaining bunny enemies. The UFO will move erratically in the final phase. Try to use your rocket when you are in the middle of the shadow. If you don’t attack the saucer quickly, then he will send more explosive enemies.
Once you manage to hit the UFO for the third and final time, the fight will end.