This level is only available when there is a Speedy Comet in orbit. The comet will appear at random, but you need to have at least completed the Dino Piranha level in Good Egg Galaxy first.
This level is identical to the Dino Piranha level, therefore the Dino Piranha level guide is a good place to get a walkthrough of this comet level. The big difference is that you only have four minutes to complete this comet level. That means you don’t want to be lingering collecting Star Bits or fighting unnecessary enemies. Just jump through each planet and make sure to leave yourself with at least a minute and half for the boss. You can defeat it in less than 30 seconds, but you’re better off giving yourself a bit more leeway during this fight by speeding through the rest of the level.