If you are wondering who Dr Katamari is, it's the cat with the weird face. Talk to it to play the two levels needed
The Doc wants friends, so the first time playing the level will involve rolling up lots of animals (friends).
Talk to the cat again later and play it again, this time rolling up about 100 friends in the shortest amount of time. There's plenty in the level so it is not a 100% thing like some levels. Once you beat both versions of the level, this should unlock upon returning to the menu area