There are three instances where fans like to consider that Batman defeated Superman in a fight, and they are Hush, Tower of Babel and The Dark Knight Returns.
Now, the first two are actually disputable. But the third one isn't.
In Hush, Batman only fought Superman (who was struggling against Poison Ivy's control) in order to distract him long enough for Catwoman to kidnap Lois, and force Clark to break free of Ivy's control. After, Batman inflicted some damage, Superman was about to finish things and crush Batman with a car until Bruce told him to look up to see Lois falling, therebye ending the fight. While Batman did beat up and basically own Superman in awesome fashion, he did not really "defeat" him, therefore Hush, does not count as a victory for Batman.
In Tower of Babel, while it is true that Batman's plans were responsible for Superman's defeat, it was not Batman who executed these plans, which were additionally modified by Ra's Al Ghul. Also, Batman was still experimenting the Red K that was used to defeat Clark, and his research was not 100% complete. So, while the story showed that Batman is fully capable of defeating Superman (and the rest of the Justice League), here it wasn't even a fight between the two, therefore it does not count as a victory for Batman (though it hints at potential victory somewhere down the road, but that's all we have, a hint, not an actual victory).
As most of you know, in the Dark Knight Returns, written by Frank Miller, Batman, using ten years of prep, help from Green Arrow and Robin, and an advanced armor, fought Superman, who was still recovering from a nuclear explosion in a climatic battle, and the undeniable result of that fight is a victory for Batman.
Here's the deal. Was the fight fair? No. Was Superman well written? No. Does this fight count as a valid answer to the question "Can Batman defeat Superman?"? No. Was Frank Miller, an admitted Superman hater, being unbiased? No. However, do all these things change the intended outcome of the fight, which was Batman defeating Superman? No. The truth is, despite all of these elements, which give Batman an unfair edge, it is clear that Batman defeated Superman, as intended, yet to this day, people still believe that Batman lost that fight, which is ludicrous.
As Stan Lee once said, the person who wins the fight, is the person that the writer wants to win. Guess who Frank Miller was pulling for...definitely not Clark! Miller wrote that fight with the specific intention of having Batman defeating Superman, yet people still want to dispute what the writer INTENDED to accomplish with some mind boggling arguments. For example:
- "The fight ended with Batman "dying" from a heart attack, with Superman holding his seemingly dead body. Therefore Superman won." No, the fight ended with Batman holding a bleeding and incapacitated Superman by the throat, and telling him that he wants him to remember the one man who beat him. The heart attack, (or fake heart attack), took place AFTER Superman's defeat. To put it in Mortal Kombat form, Batman defeated Superman, and the announcer says FINISH HIM, but instead of performing a Fatality, Batman performed a Hara-Kiri instead.
- "The fight ended with Batman having several broken ribs, while Superman only had a bleeding nose and a few bruises. Broken ribs is a much worse injury than a broken nose therefore Superman wins." No, let's put aside the fact that comparing battle damage in comics to real life injures is ridiculous, in comics, the loser of the fight is the one who is fallen and incapacitated, while the winner is the one who is standing tall, holding the other by the throat and giving an I beat you speach without any form of rebuttal by the fallen one. That person is Batman.
- "The fight was unfair, one sided prep, extra help, poor writing, biased writer, and weakened Superman who was holding back." All true. With all those elements in place, why is even a debate that Superman won? It is clear that Miller wrote this to stack all the odds against Superman and ensure his loss. Just because Batman cheated and the fight was unfair, doesn't mean that it doesn't count as a Batman victory. This isn't a real life sport, there is no disqualification, there are no rules. There is a winner and loser. I'll give an example. In Knightfall, Bane fought Batman in the Bat-Cave after he has fought and put down almost his entire rogue gallery while he was injured, sick, physically and mentally tired to the point where he could barely walk. It was an unfair fight in its fullest, yet the outcome is never in question, Bane defeated Batman and broke his back.
Here on CV, in the Dark Knight Returns story arc page, it is stated that "Batman lost" which is false. When a writer writes something with a specific goal, it should not be disputed, weather is "right" or "wrong" is irrelevant. If you ask Miller himself who won that fight, he'll gleefully tell you that it's Batman, so who are the fans to dispute what the writer claims about his own work? I do not consider it as a valid "Batman defeats Superman" feat in a battle forum but that does not means it did not take place.
Please excuse the long post, but I'm still reading comments that claim that TDKR fight is not considered a win for Batman, so it's just an issue that needed to be cleared up.