Well, in a Star Wars - based 'protagonist x antagonist fanfiction', you could have Luke Skywalker (protagonist) and Darth Vader (antagonist) in a story where Vader spares Luke's life in a different way than in the original. In a Hunger Games fanfic, Katniss (protagonist) and President Snow (antagonist) could be in a situation where they have a conversation that changes their relationship dynamic. Also, in a Naruto fanfiction, Naruto (protagonist) and Orochimaru (antagonist) might end up in a strange alliance against a new and powerful enemy.
A 'protagonist x antagonist fanfiction' example could be from the world of Sailor Moon. Sailor Moon (protagonist) and Queen Beryl (antagonist) could be in a fanfic where they are transported to a modern - day Earth and have to figure out how to get back to their own world while dealing with their natural enmity. Another instance could be in a Supernatural fanfic, with Sam and Dean Winchester (protagonists) and Lucifer (antagonist) in a situation where Lucifer is temporarily trapped in a human form and has to rely on the Winchesters for protection. And then there's a Twilight fanfiction where Bella (protagonist) and Victoria (antagonist) are in a situation where they have to team up to fight a new breed of vampires.
One example could be a Harry Potter fanfiction where Harry (protagonist) and Voldemort (antagonist) have an unexpected encounter in an alternate universe and are forced to work together. Another could be a Batman fanfiction with Batman (protagonist) and the Joker (antagonist) in a situation where they have to rely on each other's skills to survive a greater threat. A third example might be from the Lord of the Rings, with Frodo (protagonist) and Sauron (antagonist) in a scenario where Sauron has a moment of doubt and Frodo tries to exploit it.
First, understand the characters well. Know their motives, strengths, and weaknesses. For example, if your protagonist is a superhero, know what makes them heroic. Then, create an interesting scenario that brings the protagonist and antagonist together in a new way. Maybe it's a shared goal they didn't expect. Also, build tension. Let the natural conflict between them simmer and evolve as the story progresses.
An organization that wants to control or eliminate any form of magic or special abilities could be the antagonist. Since in this fanfiction, if Will has certain powers and Gideon is involved with him, the organization would target them both to maintain their idea of a 'normal' world.
Maybe a tech - based villain who can control and disrupt Metalman's systems. This villain could see Metalman as a threat to his plan of world domination through technology. Iceman would then have to use his powers to keep the villain at bay while also helping Metalman regain control of himself. The dynamic between the two heroes would be tested as they face this new and dangerous enemy.
It could be a rogue ninja from a forgotten clan who wants to steal the unique powers of Naruto, Naruko, and Satsuki. He sees their combined potential as a threat to his own evil plans of taking over the ninja world. This antagonist might have some ancient and powerful jutsu that the three heroes have to figure out how to counter.
Maybe an evil organization that wants to use Naruto's power and the connection he has with Kushina for their own dark purposes. They see Natsumi as an obstacle in their plan because she is always by Naruto's side. This organization could be experimenting with dark jutsu and need Naruto's chakra and Kushina's latent abilities (passed on to Naruto) to complete their evil experiments.
One option could be Kaguya from the Naruto universe. Her god - like powers would pose a great threat to Bayonetta. She could be trying to expand her influence into Bayonetta's world, seeing it as a new place to conquer.
In a different take, a new character could be introduced as the main antagonist. Maybe a criminal mastermind who teams up with the Joker specifically to target Robin. This new character could have a personal vendetta against Robin or see him as a key to achieving some greater evil plan, and the Joker is just a means to an end in this scenario.
It could be Kaguya Otsutsuki. Since she has powerful abilities and a thirst for power, she would see Kefla's power as a threat and Naruto's influence as something to be eliminated. She might try to manipulate events to turn the ninja world against Kefla and Naruto.
It could be a dark wizard who wants to capture the nymph for her powers. He sees the nymph's connection to nature and wants to use it to gain ultimate power in the Naruto world.
It could be a rogue ninja who has also discovered a way to harness the power of Amaterasu in a corrupt way. This ninja might want to use the power to take over the ninja villages and Naruto stands in his way.