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.
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.
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.
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.
A fanfic about Batman and Catwoman proposing could have different tones. It could be a light - hearted take where they joke around during the proposal. Or it could be a very serious and emotional one. For example, after a big battle where they almost lost each other, Batman realizes he can't live without Catwoman and decides to propose. Catwoman, who has always loved Batman but was afraid of commitment, finally says yes, seeing that he is truly committed to her.
One possible plot could be that Catwoman discovers she's pregnant and has to decide whether to tell Batman. She might be worried about how he'll react, considering their complex relationship. Maybe she tries to keep it a secret at first, but as the pregnancy progresses, it becomes harder to hide. Batman, on the other hand, might start to notice some changes in her behavior and become suspicious.
In a 'Catwoman whips Batman' fanfic, it could be a scenario where Catwoman has been misjudged by Batman. So, she uses her whip to fend him off at first. But as the story progresses, they start to understand each other better and it becomes a story of two complex characters finding common ground, with the whip being a symbol of her power and independence.
Well, it could start with Batman finally realizing his deep love for Catwoman. Maybe they decide to have a secret wedding to avoid their enemies finding out. Their friends from the Gotham underworld and Batman's allies could be in attendance, creating a very unique mix of guests at the wedding.
One of the sweetest moments could be when they are on a rooftop under the moonlight. Batman, usually so stoic, lets his guard down completely as he holds Catwoman close. They might share a soft, quiet conversation about their lives outside of the crime - fighting and capering, and in that moment, their connection deepens.
Well, it could be a story full of action and drama. Maybe they would have to face all their enemies together as a married couple for the first time. Their wedding could be a secret affair in Gotham, with only a few trusted allies in attendance.