Batman fights Superman? You betcha. More than once even. You may have heard that an older Batman battles Superman in The Dark Knight Returns (without Kryptonite!). However, there is another instance where they fought that you may not have heard of: Batman Hush. Have you ever asked yourself who would win? Time to find out.
In the comic Batman: Hush, Superman is put under Poison Ivy’s Spell and ordered to kill Batman. Batman may not have powers, but he doesn’t need them. Batman leads Superman into tunnels where he knows Superman cannot track him. Then he takes out his Kryptonite ring and beats the crap out of him. The fight continues, however I would rather not ruin the details. We have all dreamed about the Batman vs Superman scenario, which is why you should read it firsthand.
Should any of this be a surprise though? Superman is powerful, and nothing can stop him, except for a green rock that happens to instantly make him more useless than Justin Beiber. Just stab him in the heart with a sharp slab. It’s so easy, a caveman could do it. Which is what Batman is thinking as glowing rock sinks into Superman’s face.
If you are interested in Batman beating the crap out of Superman, you can get the novel here. However, I think that the concept of Batman vs Superman should be enough reason to give it a read.
Also do not forget that there was another Batman vs Superman scenario where Batman had to kill Superman. Read about it here.