You win any mission by defeating the enemy homeworld. You just do it with flair when it also is the planet to provide you the 60% control you would otherwise need to win the mission.
Space Hamsters and Sharks are tough. I can’t remember if it is the rabbits or bees that have the commander with the ability to destroy a space monster after losing to it twice. My bee campaign got a lot easier after I found a helmet that makes all monsters ignore your fleet.
I just lost my technoslug campaign in part due to a Disaster that threw a space hamster onto my homeworld, I was able to beat it eventually, but still lost the mission because the enemy ultimately conquered my homeworld. You lose any mission if the enemy conquers your homeworld.