Maybe a 'Shadow Manipulation' quirk. It would fit his dark and stealthy nature. He could use shadows to hide, move around undetected, and even attack his enemies from unexpected angles. It would be like an extension of his ability to disappear into the night in Gotham.
He could have a quirk like 'Enhanced Intellect', which would further boost his already incredible detective skills. This would make him able to analyze situations even faster and come up with strategies on the fly.
A quirk like energy absorption might be cool for Lucy. She could absorb different types of energy, such as heat, electricity, or even the kinetic energy of an attack, and then release it back in a more powerful form. This would give her an edge in combat and make her a formidable character.
He could have a 'Ninja Arts' quirk. This quirk would allow him to perform all the ninja techniques he knows from Naruto, like the Rasengan or Chidori. His Sharingan could be an additional aspect of this quirk, enhancing his ability to learn and adapt to other quirks he encounters.
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.
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.
Perhaps a 'Healing Aura' quirk. Given Sakura's medical skills in Naruto, in the MHA fanfiction, she could have a quirk that emits a healing aura. This aura could not only heal physical wounds but also have an effect on quirks that have been damaged or overused. It would make her a valuable asset in battles and in hero agencies, as she could both fight and heal her comrades.
He could have a 'Rage Quirk' that makes him stronger the angrier he gets, which would be in line with his character in Doom. When he's in a fight, his anger just builds and builds, and his physical strength and combat abilities skyrocket.
Tsuna's quirk, if we assume his Dying Will Flames are his quirk in the MHA universe, would likely be classified as an emitter type quirk. He could use his X - Burner attack as a long - range offensive move against villains. His hyper intuition could also be a part of his quirk, allowing him to predict his opponents' moves in battle. This would make him a valuable asset in hero teams, especially in complex battles where strategy is key.
One cool quirk idea could be 'Shadow Mimicry'. The user can blend into any shadow and move freely within the shadow realm, also being able to mimic the actions of those whose shadows they are in. It gives a lot of stealth and surprise attack possibilities in a fanfiction.
Iron Man's suit could potentially be considered a 'quirk' in the MHA universe. It would be a very powerful one at that. He could use his repulsor beams and various other gadgets to combat villains. Also, his ability to constantly upgrade and improve his suit would make him a formidable force. For example, he could adapt his suit to counter the different quirks of villains, like creating a device to nullify a villain's teleportation quirk.
A great fanfiction idea would be to have some of the My Hero Academia students train with Batman. He could teach them his stealth and combat techniques. This would be especially interesting for characters like Todoroki. Batman could also help them understand the importance of psychological warfare against villains. In addition, there could be a plot where a new villain emerges in the My Hero Academia world, and Batman has to use his knowledge of Gotham's villains to help the heroes figure out how to defeat this new threat.