Batman in the My Hero Academia world would likely be a bit of an outsider at first. His dark and brooding nature might contrast with the more colorful and often optimistic characters in MHA. However, his intelligence would be highly respected. He could use his detective skills to help solve some of the mysteries that pop up in the MHA world, like the origin of certain quirks or the identity of villains who are hiding in plain sight. And his martial arts expertise would make him a formidable opponent in battles against villains.
In a My Hero Academia Batman fanfiction, Batman could bring a whole new perspective on heroism. In MHA, the concept of heroes is somewhat based on having a quirk and using it for good. Batman, on the other hand, shows that you can be a hero without superpowers. He could inspire characters like Izuku Midoriya, who initially didn't have a quirk but still had the drive to be a hero. Batman might also introduce new technology and ways of fighting to the MHA world, shaking up the traditional ways heroes and villains interact.
Batman would be an outsider with unique skills. His martial arts expertise and detective skills would set him apart. He could start by observing the heroes and villains in this new world, learning about quirks.
Batman doesn't have powers like the characters in MHA, but his skills would still be extremely valuable. He could be seen as a sort of 'Quirkless' hero, much like Izuku was initially. His physical conditioning, martial arts mastery, and detective skills would set him apart. He might be able to outwit many of the villains using his intelligence.
Sakura Haruno might enter the MHA universe through some sort of multiverse portal. Once there, her strong - willed and determined nature would make her a great hero - in - training. She could learn to use her physical strength, which she had developed in the Naruto world, in combination with a new MHA - style quirk. For example, she could have a quirk that enhances her strength even further when she focuses her chakra (or a similar energy concept in MHA). This would make her a formidable force against villains.
One idea could be Batman somehow getting transported to the Boku no Hero Academia universe. He could use his detective skills and gadgets to help the heroes there. For example, he might be able to analyze the quirks in a way the local heroes haven't thought of before.
In a fanfiction scenario, the Hulk might be a result of a secret experiment by the League of Villains to create an ultimate weapon. But instead of being fully controllable, he breaks free and becomes a wild card in the power dynamics of the My Hero Academia world. His presence would disrupt the existing balance between heroes and villains as everyone tries to either control or destroy him.
In fanfiction, Broly might be a villain who comes to the My Hero Academia world seeking a worthy opponent. His raw power would pose a huge threat to the heroes, and they'd have to figure out how to stop him without getting killed.
Well, Goku's super strength and his ability to constantly power up could be a huge asset in the My Hero Academia fanfiction world. He could be like an otherworldly hero with his Saiyan powers. His Kamehameha wave would be an extremely powerful quirk - like ability. Maybe he could be a visiting hero from another dimension, coming to help out in the battles against the villains in the My Hero Academia universe.
Well, one way could be that Ichigo arrives in the My Hero Academia world through some sort of interdimensional portal. His powers, like his Soul Reaper abilities, would be seen as a very unique and powerful quirk. He might end up at UA, either as a student or a guest instructor. His strong sense of justice would align well with the values of the heroes in that world.
Deadpool would be a wild card. His regenerative abilities would make him seem like he has a quirk similar to Recovery Girl's but on steroids. He'd likely not follow the normal hero - society rules. For instance, he might start fighting villains in the middle of a civilian - filled street just because he felt like it. His presence would also disrupt the power balance as he has a vast array of weapons and combat skills that are not typical in the My Hero Academia world.
Honestly, there's hardly any link. My Hero Academia is a Japanese manga with its own unique world and themes, while Batman is a well-known DC Comics character with a separate lore and fan base. The two have little to do with each other.