Perhaps Batman has teamed up with some of Superman's other foes who have knowledge of his weaknesses. For example, Lex Luthor could provide Batman with technology or information that gives him the edge. Also, Batman might use psychological warfare on Superman, playing on his insecurities about being an alien among humans.
One idea could be that Batman discovers a new Kryptonian weapon that Superman unknowingly has a weakness to. This weapon was hidden on Earth long ago by a rogue Kryptonian. Batman then has to decide whether to use this knowledge to defeat Superman or find a way to help Superman overcome this potential threat together.
A cool plot could be that a powerful alien race arrives on Earth and offers a deal to the world leaders. Batman is suspicious of their motives and starts investigating. Superman, on the other hand, is more open - minded at first. This causes a rift between them. As Batman uncovers more evidence of the aliens' true intentions, he has to convince Superman. In the end, they join forces to stop the aliens from taking over the Earth.
A really cool plot could be a 'what if' scenario. What if Superman was raised in Gotham instead of Metropolis? How would his powers and values be different? And how would Batman react to having a super - powered being in his city from the start? In this fanfic, we could explore their relationship in a completely new light.
One plot idea could be that an otherworldly threat emerges that only their combined powers can stop. They have to put aside their differences and work together seamlessly. For example, a powerful alien race plans to invade Earth and they need to use Batman's strategic mind, Superman's super strength and Wonder Woman's combat skills.
Lex Luthor is often an interesting character in such fanfictions. He might be the one pulling the strings behind the scenes, fueling Batman's distrust of Superman. Another could be Alfred. His wisdom and influence on Batman can add depth to the story. He might try to talk Batman out of fighting Superman or help him in a more covert way. And then there's Wonder Woman. She could be caught in the middle, trying to mediate between the two or having her own motives for getting involved in their conflict.
One idea could be a story where Batman and Superman have to team up to stop a powerful new villain who is using kryptonite - based technology. This would put Superman at a great disadvantage and force Batman to use his detective skills to find a way to neutralize the threat.
Alfred is always a likely ally. His knowledge and experience can provide valuable support to Batman. Also, Oracle (Barbara Gordon) could be an important ally, using her hacking skills to disrupt any technology Superman might use or to gather information.
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.
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.
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.