What type of beer is best for beer battered fish?
The primary use of beer in a beer batter is its alcohol, which disrupts gluten formation and needs less heat than water to evaporate, improving the texture of the final crust. For flavor, most recipes using beer do best with a malty, low-bitterness beer, like a marzen, scotch ale, or (maybe) amber ale. Highly-hopped "put hair on your chest" IPAs are a bad idea: you don't want that bitterness. Hefeweizen would be fine.

A couple of commenters mentioned the carbonation as being an important factor. I suspect that it isn't. The volume of gas generated by evaporating the water in the beer will dwarf the amount of CO2 being released, even in the most highly carbonated of beers.