1. The Dark Knight Returns is not in continuity.
2.
Batman didn't fight Superman, it was more like Batman running away and doing small moves to stall Superman so Catwoman can capture Perry White, Jimmy Olsen, Lois Lane, or Clark Kent so Superman could fight his mind control from Poison Ivy. Also, Superman was holding back.
It was in three issues, Superman #219, Action Comics #829, and Adventures of Superman #642. He thought that Batman was Brainiac killing Lois, Perry, Jimmy, and Lana; Darkseid enslaving Lois and killing her, and Ruin killing Lois. Superman did not hold back and fought Batman in rage. He would have killed Batman if Batman did not utilize the Watchtower's defense systems and Wonder Woman's intervention.
Batman was severely injured. He had to be healed with the Purple Healing Ray, Superman's fingerprints were impressed on Batman's flesh, his ribs were broken and were cracking whenever he breathed, he was burned by Superman's heat vision. He had to be carried back to the Batcave.
Superman later fought Wonder Woman in Wonder Woman #219, thinking that she was Doomsday killing Lois.