It could be Orochimaru. Imagine if he also found a way to cross over into the Avatar world. With his knowledge of dark jutsu and his desire for power, he would be a formidable antagonist. He might try to use the bending abilities for his own evil purposes and also target Naruto because of his immortality, seeing it as something he could steal or use to further his plans.
Maybe a combined form of Madara Uchiha and Ozai. Madara's power - hungry nature and Ozai's thirst for domination could merge into one terrifying antagonist. This combined villain would want to rule both the Naruto world and the Avatar world. They would see Naruto's immortality as a challenge and the Avatar as a threat to their plans of total control. They would start wars in both worlds and force Naruto and the Avatar to team up to stop them.
In the 'immortal naruto avatar fanfiction', the main antagonist might be a corrupted Avatar. This Avatar, instead of maintaining balance, wants to use Naruto's immortality to become an all - powerful dictator. He or she would have the bending abilities of an Avatar and the knowledge of how to use them in devious ways. This would put Naruto in a difficult position as he has to either stop the Avatar or find a way to redeem him/her while also protecting his own immortality.
Another possibility is a powerful spirit from the Avatar world that has been corrupted by the introduction of Naruto - like powers. This spirit could resent the intrusion of this new power source and seek to destroy anyone associated with it. It might have unique abilities that combine the spiritual magic of the Avatar world with the raw power of Naruto's chakra, making it a formidable foe.
It could be a rogue ninja who has somehow harnessed the power of the Crimson Avatar in a dark and corrupted way. This ninja could use his powers to try and take over the ninja villages, believing that the traditional ninja ways are weak. He might see himself as a new kind of leader, using fear and his overwhelming Crimson Avatar powers to rule.
Perhaps an ancient evil that has been sealed away in the empire for centuries but is released due to the chaos of the crossover. This entity could be more powerful than any foe the Naruto characters have faced before, forcing them to find new ways to fight.
A group of rogue shinobi and some of Daria's school bullies could team up. The shinobi would give the bullies some ninja powers, and together they would cause trouble in both worlds. This group would be difficult to deal with as they combine the physical strength of the shinobi with the local knowledge of the bullies.
Another possibility is a corrupted dragon spirit that has been awakened due to the mixing of the two worlds. This spirit could be spreading chaos and trying to destroy both the ninja world and the dragon world. Naruto would have to figure out a way to stop it, as it has powers that are beyond what he has faced before.
It could be an evil ninja from Naruto's world who somehow gains Kryptonian - like powers. He becomes power - hungry and decides to take over both the Naruto world and Supergirl's world. His knowledge of ninja techniques combined with super strength and other abilities would make him a formidable foe.
Madara Uchiha would also make a great antagonist. Imagine if he was resurrected and saw Naruto with Samehada as a threat to his plans of creating a new world order. He would use his Sharingan and Rinnegan powers to try and take Samehada from Naruto, believing that with it, he could easily defeat all who oppose him and reshape the ninja world according to his will.
Maybe another kitsune who has gone bad. In the fanfiction world, there could be a rogue kitsune who sees Naruto as a threat. This antagonist kitsune might be jealous of Naruto's power or his connection to the human world. They could try to undermine Naruto's attempts to protect the village or his friends.
It could be a powerful dark spirit from Kagome's world that somehow manages to cross over to the Naruto universe and starts causing chaos. This spirit might be immune to normal ninja attacks and require Kagome's spiritual powers to be defeated.