Skipper hasn't been fully completed, so it isn't possible to unlock him just yet. Right now, all the playable characters have been pre-unlocked, usually indicated with a blue icon covering in the CSS. This means they are unlocked for the sake of players being able to test and mess around and whatnot. In the next next update (0.2.5), I'm going to relock Dr. Blowhole, Bessie, Patrick, and Sheen; and they will become the first truly unlockable characters.
Skipper is in development right now, alongside Kitty Katswell and Chum Chum. He will be available soon!