One possible storyline could be that Batman is on a mission in the Amazon and crosses paths with Hippolyta. They initially have a misunderstanding as Batman's methods seem strange to Hippolyta, but as they get to know each other, they find they have a mutual respect for justice. Batman learns about the Amazonian way of life and Hippolyta becomes intrigued by Batman's detective skills.
It could also be a love story of sorts. The contrast between Batman's dark and brooding nature and Hippolyta's regal and strong - willed personality could create an interesting dynamic. They might meet during some sort of inter - dimensional crisis and find themselves drawn to each other, defying the odds and the differences in their worlds.
One possibility is that they would initially be on guard around each other. Batman is used to the dark and gritty streets of Gotham, while Hippolyta is a powerful Amazonian queen. They might start off sizing each other up, Batman analyzing her as a potential threat or ally, and Hippolyta seeing him as an outsider from a different world. Eventually, they could find common ground in their sense of justice. Batman's fight against crime in Gotham and Hippolyta's leadership in protecting the Amazons both stem from a desire for fairness and safety. So they might team up to take on a greater threat that endangers both their worlds.
Maybe Batman takes Billy Batson under his wing to help him deal with his newfound powers. Billy is just a kid who suddenly has the power of gods, and he might be a bit overwhelmed. Batman, with his experience in handling complex situations, could guide Billy on how to control his powers and not let them go to his head. He could also teach Billy about the responsibility that comes with great power.
Maybe the daughter discovers a secret conspiracy in Gotham that involves both her parents' past enemies. She has to use her unique combination of skills, like Batman's detective work and Catwoman's acrobatic abilities, to uncover the truth. Along the way, she forms her own team of allies, some from the side of the law and some from the fringes.
Another option is Fanfiction.net. There are a large number of fan-written stories there. However, the search function might not be as refined as AO3. So you may need to sift through a few results to find the really good ones about Batman and Hippolyta's romance.
One interesting storyline could be a crossover where Naruto somehow ends up in Hippolyta's world. He might use his ninja skills to help the Amazons in their battles, like using his shadow clone jutsu to create distractions during an enemy attack.
The plot is crucial. Maybe it could involve some sort of cross - dimensional adventure where Batman and Hippolyta are brought together. Or perhaps a situation where they have to team up to face a common enemy, and during that time, their relationship blossoms. It also needs to have a good balance between action, dialogue, and the romantic elements. For example, their first meeting could be filled with tension and mutual respect that gradually turns into something more.
The plot could start with Batman investigating some strange occurrences that lead him to the hidden world of the Amazons. When he meets Hippolyta, there is immediate tension. But as they talk, they realize that there are dark forces at work that are threatening both Gotham and the Amazonian homeland. They then form an uneasy alliance. As they work together, they face challenges like different combat styles. Batman has his gadgets and martial arts, while Hippolyta has her Amazonian training. Along the way, they start to respect each other more and more, and by the end, they have not only defeated the common enemy but also have a new - found respect for each other's worlds.
In a fanfiction, it could be that a scientific experiment gone wrong in Gotham creates a mutant - like creature that has super strength and intelligence. This creature targets Batman as it sees him as a threat to its new - found power in the city. After a long and brutal battle, the creature overcomes Batman and kills him.
A storyline could involve Nightwing being framed for a crime in Gotham. Batman, believing the evidence at first, tries to bring him in. Nightwing, of course, resists as he is innocent, and this leads to their fight. As the story progresses, they both realize there's a bigger conspiracy at play.