The Pokémon Staryu does not evolve based on levels. Using a Water Stone helps Staryu evolve into Starmie, which is its final form. Levels are important, however, as this Pokémon obtains additional powers as it scales up.
Staryu learns a series of moves as it gains experience and levels up, but it stays in the same physical form. At level one, it possesses only the Harden move, although defensively it is difficult to harm Staryu. At the fourth level, it manifests the Water Gun specialty. Staryu does not gain a new skill for every single level; sometimes, new moves come in multiples of two, three or four levels.