In this kind of fanfic, the villains' roles would be very diverse. Bane, for instance, might see the zombies as a new challenge to overcome and prove his strength. He could either fight them head - on or try to control them. Catwoman, being a more morally ambiguous character, could go either way. She might steal supplies from survivors or she could help Batman if she thought it was in her best interest. The villains' actions would add a lot of complexity and twists to the story of a Batman zombie apocalypse.
The villains could either be a bigger threat or an unexpected ally. Some villains might see the zombie apocalypse as an opportunity to take over Gotham without Batman interfering. But others, like Poison Ivy, might actually try to find a way to stop the zombies as they don't want their 'playground' to be destroyed.
Well, Batman is a master of stealth. In a zombie apocalypse in this fanfic, he could easily move around undetected by the zombies. He has a wide array of gadgets that could be useful. His grappling hook, for example, could help him reach safe places above the ground where zombies can't reach. Also, his batarangs could be used as both a weapon to take out zombies from a distance and as a distraction.
Toga might be interested in the zombies in a different way. Since she has a fascination with blood, she could study the zombies to see how their blood or 'undead' state works. However, other villains might just be in it for themselves. Dabi, for example, might just burn his way through the zombie hordes without much thought for a grand plan. He'd be more focused on his own survival and causing chaos.
A possible plot could be that an unknown enemy uses a powerful jutsu that accidentally creates zombies. The story could start with Naruto and his friends in Konoha noticing strange behavior among some villagers. As the situation worsens, they realize it's a zombie outbreak. They then have to band together, find out the source of the outbreak, and try to stop it while also protecting the remaining survivors.
Sonic's speed allows him to be a great scout. He can cover large areas in no time to find safe places or look for resources. His ability to spin dash can also be used as an offensive move against zombies. Tails, on the other hand, could use his two tails to fly and get a better view of the surroundings. He could also use his knowledge of mechanics to jury - rig weapons from the debris around. For instance, he might make a makeshift flamethrower using some old parts and a fuel source, which would be very effective against zombies.
The Joker's gas can be a major source of conflict. It can put the Batfamily in immediate danger, forcing them to find antidotes or ways to avoid it. For example, the gas could make them hallucinate, seeing their worst nightmares come to life.
The puck in Batman comics often serves as a unique gadget or tool for Batman in his crime-fighting endeavors, sometimes used to surprise or outsmart his foes.
In Batman comics, Victor can have various roles. Sometimes he's a villain with unique motives and schemes against Batman. Other times, he might be an ally with a complicated past and questionable loyalties.
The dog might be a sidekick or a helper to Batman in some storylines, providing additional support or creating interesting plot twists.
The therapist in Batman comics often helps him deal with his inner demons and psychological stress. They provide a source of support and guidance for him to stay sane in his crime-fighting endeavors.
Alfred is Batman's trusted butler and confidant. He provides support, helps with detective work, and takes care of Wayne Manor.