One idea could be that Batman is turned into a cat by a villain's new experimental device. As a cat, he has to rely on his natural feline abilities like stealth and agility to still protect Gotham. For example, he could use his cat form to get into small spaces in buildings to gather evidence or spy on criminals.
Well, he might find it really hard to operate his Bat - gadgets as a cat. His paws are not made for pushing buttons or typing on keyboards. So he has to figure out a way to adapt. Maybe he uses his cat claws to scratch out messages for Alfred to understand what he wants to do.
Another possibility is that Batman is experimenting with a new technology to enhance his abilities. He creates a device that is supposed to give him the ability to fly like a bat. However, something goes wrong during the testing phase. The device fuses with his DNA, and he starts to turn into a bat. He has to deal with the physical and mental changes, all while trying to keep it a secret from his allies like Alfred and Commissioner Gordon.
Batman would be heartbroken. He has trained Robin and sees him as a partner and almost like a son. He would first try to talk to Robin, to find out what made him turn evil. He would hope that he could reason with Robin and bring him back to the good side.
Well, often he has to figure out how to communicate. He might try to use his body language in creative ways to get his friends' attention. For instance, he could lead them to where danger is by pawing at their feet and then running in the direction they need to go.
Well, obviously Izuku is one of the main characters, even when he's turned into a cat. His friends like Bakugo and Ochaco are also likely to be main characters. They would be the ones trying to figure out what happened to Izuku and how to turn him back. And maybe All Might could also be a main character, if he gets involved in the whole situation to help his young protege.
Another plot could be that he is exposed to some sort of mind - controlling substance or technology. The enemy could be using it to turn him against Gotham. Under this influence, he starts to see his friends as foes. He could begin to attack the Bat - family and other superhero allies. His actions would be erratic and violent, and the city would be in chaos as they try to figure out what happened to their hero and how to stop him.
Perhaps it's due to a psychological breakdown. Batman has endured so much trauma over the years. The constant fight against crime, the loss of loved ones, and the never - ending battle with his inner demons could all take a toll. One day, he just snaps. His mind can no longer handle the pressure, and in an attempt to escape from his own tortured self, he subconsciously adopts the persona of the Joker, as the Joker seems to have no such moral and emotional burdens.
One great 'Hermione turns into a cat' fanfiction is 'The Feline Transformation of Hermione'. It delves into how her friends react to her new form. Another is 'Hermione's Cat Adventure' which focuses on her exploring the wizarding world from a cat's perspective. There's also 'When Hermione Became a Cat' which has a really interesting plot about her trying to find a way to turn back while dealing with the mischief cats usually get into in Hogwarts.
A more emotional plot could be Izuku as a cat being found by a villain who initially wants to use him against the heroes. But over time, the villain starts to develop a strange bond with the cat - Izuku. This then makes the villain question his own motives and actions.