During the Creature phase (right out of the tidal pool), you can get additional parts for your creature by impressing the alpha versions of the fellow inhabitants of your world. When you first approach them, sometimes others of their species will join in the game. The more of them there are, the more difficult it can become. Push the alpha away from the nest, and try to solo it out so that you only have to deal with him dancing, singing, etc. against your crew of followers.