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.
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.
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.
For Batman, his character could be developed by showing more of his internal struggle. In the Arkham Knight scenario, he's facing a lot of challenges. Maybe he starts to question his no - kill rule more when he sees the destruction the Arkham Knight is causing. With Catwoman, her thieving skills could be explored in more detail. She could use her skills not just for personal gain but also to help the people of Gotham in a more subtle way.
The key events include Scarecrow's plot to take over Gotham with fear toxin, which forces the evacuation of the city. The Arkham Knight's attacks on Batman and his allies are important. And Batman's journey to discover the Arkham Knight's true identity while also dealing with the psychological effects of the fear toxin and his memories of Joker.
One key event is when Scarecrow first releases his fear toxin in Gotham, causing widespread panic. Another is the revelation of the Arkham Knight's identity, which is a big shock in the story. Also, Batman's battles with the various villains like the Penguin and his fight to stop their criminal activities during the chaos are important events.
One key element is her thieving nature. She's constantly looking for valuable items to steal. Another is her relationship with Batman, which is a mix of attraction and conflict. Also, her involvement in the power dynamics of Arkham City, where different villains are vying for control, is important.
One great 'Batman Arkham Catwoman' fanfiction is 'The Thief and the Dark Knight'. It explores their complex relationship in the Arkham universe. The author does a wonderful job of portraying Catwoman's sly nature and her attraction to Batman. Another is 'Catwoman's Arkham Adventure' which focuses on her solo escapades within the Arkham setting, with some really cool action scenes.
Well, there's an author named ScarletPen who has written some really engaging 'Batman Arkham Catwoman' fanfictions. Their stories often focus on the emotional connection between the two characters. Another good one is GrayShadow. They are known for their detailed descriptions of the Arkham environment in relation to Catwoman's adventures. And then there's MoonlitWriter who has a unique style of writing Catwoman's character, making her both strong and vulnerable in the Arkham setting.
Well, a lot of fanfictions focus on the emotional side of their relationship. In Arkham City, they are both in a high - stress situation. A fanfiction might show how Catwoman is the only one who can reach Batman on an emotional level when he's deep in the fight against the criminals in Arkham City. She might be able to get him to open up about his fears and doubts, which is something he doesn't do with anyone else.