In this fanfiction, it could be interesting if Catwoman discovers a secret about the Arkham Knight that Batman has overlooked. She could use this knowledge to her advantage, either to make a deal with the Arkham Knight or to help Batman. For example, she might find out that the Arkham Knight has a weakness related to a certain location in Gotham that was important to his past. Catwoman could then lead Batman there to take down the Arkham Knight.
One idea could be a story where Batman and Catwoman team up to take on a new, more powerful villain in Arkham. Maybe this villain has the ability to control the minds of the inmates, creating chaos. They'd have to use their unique skills, Batman's detective work and combat abilities, and Catwoman's agility and thieving expertise to stop the threat.
One idea could be exploring how the Knightfall event affects Batman's relationships with his allies in the Arkham Knight universe. Maybe some of them start to question his methods more deeply.
One interesting plot idea could be a fanfiction where the Joker somehow comes back to life in Arkham Knight. Maybe he was only in a coma and wakes up with a new, even more deranged plan to take over Gotham. He could start by manipulating the inmates in Arkham again, creating chaos from within the asylum.
Well, a great plot idea might be delving deeper into the relationship between Batman and his rogues gallery in the aftermath. For example, how the villains react to Batman's continued presence or absence. Some might see it as an opportunity to take over Gotham, while others might be secretly glad he's still around to keep a certain order. Also, exploring the technological fallout. With all the advanced tech used during Arkham Knight, there could be some unforeseen consequences like tech falling into the wrong hands or new, unexpected uses for it.
Yes, there are quite a few. You can start by looking on fanfiction websites like Archive of Our Own. There are stories that explore Catwoman's relationship with Batman in the Arkham Knight universe in various ways, such as her adventures during the events of the game, or her backstory and how it ties into the overall Arkham Knight narrative.
A great plot idea for this fanfiction could be that Harley Quinn is haunted by the memories of her time with the Joker during the Arkham Knight scenario. Batman, noticing her distress, tries to help her. As they interact more, Harley starts to see Batman in a new light and decides to assist him in his fight against the Arkham Knight. Along the way, they face many challenges, like dealing with Harley's old gang who don't trust her new alliance with Batman, and also the Arkham Knight's devious traps. This would make for a complex and engaging fanfiction story.
Archive of Our Own (AO3) is a great place to start. It has a large collection of fanfiction, and you can easily search for Batman Arkham Knight Catwoman fanfiction there. Just use the search bar and type in relevant keywords.
Another plot could involve Weiss using her family's resources to create technology similar to what's in Arkham Knight's world to combat a new type of Grimm. And the Arkham Knight himself might be interested in this tech and try to steal it, leading to an interesting conflict and alliance between Weiss and the other RWBY characters against him.
In some fanfictions, the plotline might be that there's a hidden treasure in Arkham City that both Batman and Catwoman are after for different reasons. They start as rivals but as they face the various threats in Arkham City, like the other inmates and the corrupt guards, they realize they need to work together. This story could explore how they negotiate their differences and build a stronger bond in the context of Arkham City.
One idea could be a story where Catwoman steals a valuable item during the chaos of Gotham's post - Bane takeover in The Dark Knight Rises. Batman has to track her down, but as he does, they start to realize their feelings for each other are more complex than just hero - villain. They could end up teaming up against a new threat that emerges from the ashes of Bane's rule.