A good playing strategy is to crush all of the Eggs in one area at a time, keeping within easy readh of a Pulsar. The best way to destroy Aliens is to sit near a Pulsar until the Aliens are almost upon you. Then grab that Pulsar and go get 'em !
Use the Hyperwarp Passage to ditch Aliens. Many times they won't follow you in.
If you're having trouble with the Bonus Rounds, try going between the Alien pairs rather than around them.