At what level does Poliwhirl evolve?

Poliwhirl does not evolve at any specific level. Instead, the Poliwhirl evolves into Poliwrath when a water stone is used on it, or, alternatively, into Politoed when it is traded while holding a King's Rock. Poliwhirl itself evolves from Poliwag.

Poliwrath appears in every generation of Pokémon games, and likewise, the water stone does, too. In "Pokémon X" and "Pokémon Y," a water stone can be found on Route 8. Politoed and the King's Rock were introduced in Generation 2. Poliwrath and Politoed must be obtained through evolution in most "Pokémon" games before Generation V, but starting with "Pokémon Black" and "Pokemon White," the two can also be caught in the wild.