Batman's Lover

I don't know very much about Batman, because I didn't have access to all the comics growing up. Only recently I've watched some cartoons and movies about him. One of the best female opponents of Batman appears in the cartoon series Batman of the Future (also known as Batman Beyond), when the action takes place at a time where Bruce Wayne is an old man and he is teaching Terry McGinnis, a young man, the art of being Batman. This formidable opponent of Batman is called Curaré. She was a highly regarded member of the Society of Assassins, and despite the origin of her name, she rarely dealt in poisons. Instead, Curaré preferred a special sword which can cut through nearly anything, its edge being sharpened to only a molecule in thickness.

To me, Catwoman/Selina Kyle was the only real woman for him. Vikki Vale and Rachel Dawes came close, but Selina was the only one who could challenge Bruce.