In this fanfiction, their daughter might inherit Batman's sense of justice and Catwoman's agility. She could grow up torn between the two worlds of her parents. Maybe she'd use her skills to fight crime in a different way than Batman, with a bit more of Catwoman's slyness. For example, she could use her charm to get information from villains before taking them down.
She could be a vigilante like her father, but with a more flamboyant style inspired by her mother. Imagine her swinging through Gotham in a purple and black catsuit, using her wits and combat skills to take down criminals.
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.
Well, she could be a character who struggles with the duality of her heritage. On one hand, she has Batman's sense of justice and order, but on the other, Catwoman's more fluid view of right and wrong. This internal conflict could be a major part of the fanfic. She might also have her own love interests, perhaps a character who is neither fully on the side of the law like her father, nor a thief like her mother, adding another layer of complexity to her story.
The Penguin could be a main antagonist. He might see the daughter as a new threat to his criminal operations in Gotham. Since she has the combined skills of Batman and Catwoman, she could easily disrupt his illegal business, like his smuggling operations.
In some fanfiction, their daughter could be a powerful force for change in Gotham. She might use her parents' influence and resources in unique ways. For example, she could start a new movement to clean up the city, using her mother's charm and her father's detective skills to expose corruption and bring about real change. This would be a fresh take on the Batman - Catwoman story and add a new layer of depth to the Gotham universe.
One possible plot could be that Batman and Catwoman have a child who discovers their parents' secret identities by accident. The child might then try to use their own skills, a combination of Batman's detective skills and Catwoman's agility, to help their parents fight a new villain in Gotham.
There could be a 'catwoman kills batman fanfiction'. A possible plot could be that Catwoman is in a situation where she has to choose between saving the city and Batman. She might think that sacrificing Batman is the only way to stop a greater evil from destroying Gotham. For example, if there's a doomsday device that can only be deactivated by Batman's death and she decides to go through with it.
A possible plot could be that Catwoman discovers she's pregnant. She then has to decide whether to tell Batman or not. She might be worried about how he'll react, considering their different lifestyles. Eventually, she tells him, and they start to plan for the future. They could face challenges from their enemies who might see the baby as a weakness or a target.
In fanfiction, Batman could reject Catwoman for several reasons. Firstly, his own psychological state. He has a lot of trauma from his past, like the death of his parents. This may make him hesitant to get involved in a relationship, especially with someone like Catwoman who has her own set of issues. Secondly, Batman is a symbol of justice and order in Gotham. Associating with Catwoman, who often flouts the law, could damage his reputation. Moreover, he might believe that Catwoman will never fully abandon her life of crime, and he can't accept that in a partner.
Maybe Batman gets jealous when Catwoman teams up with another anti - hero. He's so used to being her main partner in crime - fighting (sort of), and this new alliance makes him feel left out. It would be an interesting angle to explore how his jealousy affects their dynamic.