To batter is to beat repeatedly, as if one boxer were clobbering another with blows.
Batter is one of those words with many meanings that seem entirely unrelated to each other. You can batter by hitting again and again, but there's also a batter in baseball — the guy who's holding a bat and waiting for the pitcher to throw the ball. Yet another meaning is the batter you mix up when you're making muffins, using eggs, flour, milk, and sugar. They all come from the same Latin root word, battuere, "to beat or strike."