During the Creature stage (fresh out of the tidal pool), you can get more parts for your creature by impressing the alpha versions of the fellow inhabitants of your world. When you first approach them, occasionally others of their species will join in the game. The more of them there are, the more difficulty 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.