This Seeking Tech guide will explain how you can beat the first Retro Rampage level in Astro Bot.
Use the following video as a reference:
When dealing with the bunny enemies, dodge their attempts to squash you and then attack them with a spin attack.
When the bigger bunny appears, you should first side-step his jump. You can then use another spin attack to destroy its red core.
Here is the same run again at normal speed.