Batman himself is obviously one of the most popular characters. He is the central figure and the source of the 'badass' factor in the fanfic. The Joker is also very popular as he provides a great contrast to Batman with his chaos and madness. Harley Quinn is often included as well, with her complex relationship with the Joker and her own brand of insanity. Another popular character is Robin, who represents the sidekick and the future of Batman's legacy.
Well, in 'batman badass fanfic', there might be the idea of Batman having some extraordinary combat skills. He could be shown using martial arts from all over the world in a more seamless and deadly way. Maybe he has a special move that he developed himself to take on multiple opponents at once. And then there could be a concept of a secret society within Gotham that Batman has to infiltrate. This society could have its own set of rules and power dynamics that Batman has to navigate through, adding an extra layer of mystery and danger to the story.
One interesting aspect could be the unique interpretations of Batman's character. Fanfics might explore a darker or more complex side of him that we don't always see in the official comics or movies. For example, they could show his internal struggles in more depth.
I'm not sure of specific titles off - hand, but you can start by looking on fanfiction websites. Search for ones with high ratings and lots of reviews. Usually, those are the better ones.
One great 'Percy being a badass' fanfiction is 'Percy Jackson: The Badass Avenger'. In this story, Percy uses his skills and powers in really cool and unexpected ways. He takes on powerful enemies all by himself and shows his true strength.
One example could be when he single - handedly takes on a horde of monsters in a fanfiction. His water powers create massive tidal waves that sweep away the foes. Another instance is when he uses his wits and sword skills to defeat a powerful, new - created villain in a fan - made adventure.
In certain fanfiction stories, Hermione is portrayed as a spy in the dark wizard's lair. She has to blend in, gather intelligence, and escape without being detected. She uses her wits to deceive the dark wizards, and when she's finally discovered, she uses her combat magic to fight her way out. This shows her as a really badass character, being able to handle such a dangerous and complex situation all by herself.
In this fanfiction, Hinata could be badass in a way that she challenges the village elders directly about Naruto's banishment. She argues that Naruto has been the savior of the village multiple times and his banishment is unjust. As she does this, she also showcases her new and improved combat skills, which she has been secretly honing, to intimidate those who oppose her and show that she will fight for Naruto's return.
One possible fanfiction could be that Batman is thrown into Arkham Asylum by a powerful new villain who has framed him for a series of heinous crimes. Inside, he has to deal with the inmates who are both his enemies and, in some strange way, his allies as he tries to clear his name.