Well, perhaps in the fanfiction, Naruto's world is merging with the DC world. Batman sees Naruto as an unknown variable and initially suspects him. But when Superman starts acting erratically due to a kryptonite - like substance from Naruto's world, they have to work together. Naruto's ability to sense chakra might help them find the source of the problem and defeat the 'evil' Superman. And they could all learn from each other's fighting styles and ethics along the way.
One idea could be that Naruto is somehow transported to the DC universe. He teams up with Batman against Superman who has been mind - controlled. Naruto uses his Rasengan and shadow clone jutsu to help Batman outwit Superman's super strength. Another plot could involve a tournament where Naruto, Batman, and Superman all compete, with Naruto's ninja skills being a wild card in the mix.
One idea could be that Batman and Superman are forced to team up against a common enemy from another dimension. This enemy has the power to manipulate the minds of the citizens of Metropolis and Gotham, making them turn on their heroes. Batman uses his detective skills to find the source of the mind control, while Superman has to hold off the hordes of brainwashed civilians.
One idea could be an OC who has the power to nullify Superman's powers temporarily, making the fight more evenly matched against Batman. This OC could be a scientist who has developed a special device after years of studying Kryptonian physiology.
One idea could be a story where Batman and Superman have to team up against a common enemy before their big fight actually happens. Maybe a powerful alien threat that forces them to realize they need each other's skills.
One plot idea could be that Superman is exposed to a new type of kryptonite that not only weakens him physically but also starts to affect his mind, making him a danger to himself and others. Batman, using his detective skills, discovers the source of this new kryptonite and figures out a way to neutralize it, thus saving Superman. Another could be that Superman is framed for a crime he didn't commit and is being hunted by the world. Batman, believing in his friend's innocence, uses his resources and stealth to clear Superman's name and save him from the wrath of the world.
One idea could be that Batman and Superman have to team up to stop a new villain who has the power to manipulate time. This would put their different approaches to justice to the test as they race against the clock.
Here's an idea. There could be a powerful magical artifact that surfaces in both cities. It has the power to change reality. Superman, being a man of science, is initially skeptical about its power. Batman, on the other hand, has seen enough strange things in Gotham to know it's dangerous. They have to overcome their differences in beliefs as they race against time to stop different factions in both cities who want to use the artifact for their own gain. Along the way, they also learn more about each other's worlds and form a stronger bond.
In a fanfiction, perhaps there's an apocalypse scenario where Superman is infected with some kind of kryptonite - based virus that makes him go berserk. Batman has to find a cure while also keeping Superman from causing too much damage. At the same time, they are dealing with the general chaos of the apocalypse, like gangs taking over the city and other villains trying to take advantage of the situation.
One idea could be that Superman and Batman have to team up to stop a new supervillain who has the power to manipulate time. This would force them to put aside their differences and work together in a really challenging situation.
One idea could be that they team up to fight a new supervillain who has the power to manipulate time. Batman's detective skills and the female Superman's super strength would make for an exciting combination.
Another plot could be that Batman discovers a new weakness of Superman. Perhaps it has something to do with a certain frequency or energy that Superman is vulnerable to. Batman then builds a device that emits this energy, and during their battle, he uses it to incapacitate Superman. This would be a unique take on the 'Batman defeats Superman' scenario.