I've got to rewatch the OVA. I can link youtube videos of some of her fights. I haven't quite finished the TV series, but she seems to push herself less in it and doesn't show up until the last 1/3 of it (aside from a flashback scene).
I originally watched bits of the OVA when they aired the whole thing at once on Adult Swim. After that I kept associating it with that one Beethoven song.