One possible storyline could be that Batman has to use his detective skills to find out a hidden threat to Superman before saving him. Maybe there's a kryptonite - based weapon that only Batman can detect and disable.
A cool story could be about them having a friendly competition to see who can solve a series of mysterious crimes in the other's city first. Along the way, they learn more about each other's methods and develop a deeper respect for one another. This also gives an opportunity to explore the different atmospheres and challenges of Gotham and Metropolis.
One interesting storyline could be a young Superman and Batman teaming up for the first time in a kid - friendly adventure. Maybe they are trying to stop a group of small - time villains who are stealing toys from all the kids in Gotham. They use their unique powers and detective skills respectively to track down the bad guys and return the toys.
Lex Luthor is often a main antagonist. He might be the one who sets up the situation where Superman needs to be saved, like creating a powerful weapon or a devious plan to weaken Superman.
One interesting storyline could be a redemption arc for Superman. In the Injustice universe, Superman has gone down a dark path. A fanfiction might explore how Batman tries to bring back the good in him, with lots of emotional confrontations and moral debates between the two.
A theme that frequently appears is redemption. Sometimes Batman might be in a situation because of a mistake he made, and Superman saving him is a form of redemption. Also, the theme of heroism is prominent. Superman's act of saving Batman reaffirms their status as heroes and shows their selfless nature towards each other.
One interesting storyline could be a team - up against a new super - villain who has the power to manipulate time. Batman and Batwoman would have to race against the clock to stop this villain before he changes history to his advantage.
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.
One interesting storyline could be exploring how Batman got his scars in a different way than the traditional origin. Maybe in a fanfic, he gets the scars while protecting a young orphan who later becomes his sidekick. Another could be a story where the scars are a source of new powers or a connection to an ancient prophecy.
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.