One idea could be that Batman and Supergirl team up to stop a powerful alien threat that is beyond the capabilities of either of them alone. They start off distrusting each other due to their different methods, but as they face challenges, they learn to work together and respect one another's skills.
A plot could involve a time - traveling scenario. Supergirl gets sent back in time to Gotham in the early days of Batman's career. She has to keep her identity a secret while helping Batman fight a new kind of villain that has some connection to Krypton. This forces them to work together in a very different setting than they are used to.
A plot could involve a time - travel scenario where Batman and Supergirl are sent back in time to prevent a major event that would change the future of both their worlds. They would have to work together, using their different skills and knowledge of their respective eras.
One idea could be that Batman tries to train Supergirl to better control her powers in the context of the Injustice 2 universe. He might see her as a potential force for good against the tyrannical regime. Another could be that Supergirl discovers a way to bring back the more heroic Superman she once knew, and Batman has to decide whether to trust her plan or not.
One idea could be that Supergirl and Batman team up to stop a powerful alien weapon from being used on Earth. Maybe the weapon was stolen from a Kryptonian ship and Batman uses his detective skills to find clues while Supergirl uses her superpowers to fight off the bad guys who have the weapon.
Maybe a story where the Avengers are transported to Supergirl's universe. They have to adapt to her world's rules and help her fight against a powerful villain there. This could involve a lot of world - building and character development as the Avengers learn about Supergirl's allies and enemies.
One idea could be that Flash and Supergirl team up to stop a powerful alien villain who is causing chaos across both their cities. The villain could have the ability to manipulate time and space, which would make it a real challenge for the two heroes.
One could be a Supergirl fanfic about her teaming up with other superheroes from different universes to fight a powerful cosmic villain. It would involve epic battles and interesting character interactions.
One idea could be that Raven is in danger from a new dark magic threat and Batman, with his detective skills, helps her track down the source. They start to learn from each other, Raven about Batman's human tenacity and Batman about Raven's otherworldly powers.
One idea could be exploring Bruce Wayne's early training in more detail. Show his struggles and how he overcame them. For example, his first encounters with Ra's al Ghul's League of Shadows could be more in - depth, with new challenges and characters added.
One idea could be that Robin gets trapped in an alternate dimension where the villains are in control and Batman has to figure out a way to bring him back. Another could be a story where Batman is injured and Robin has to take on a major villain alone, learning to trust his own instincts more. Maybe a plot where they encounter a new, powerful ally who turns out to have a hidden agenda that threatens Gotham.
A plot could involve Batman investigating a mystery that has ties to Themiscyra. For example, some ancient artifacts from Themiscyra are showing up in Gotham's black market. As he delves deeper, he discovers a connection to a long - lost Amazonian prophecy. Or perhaps there's a character from Themiscyra who has come to Gotham seeking Batman's help to save her homeland from an internal power struggle.