Poké Floats is unlocked by playing 200 battles in VS mode.
Poké Float is a rather unique stage. You battle on top of giant Pokémon balloons. You will fight on top of different Pokémon as the battle goes on. You have to keep up with the pace of the stage; staying on a certain float too long might cost you a stock. You should first try practicing on this stage first before engaging into actual battles. The Pokémon appearance is always the same and never random.