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.
It could be an earthbound immortal who has been corrupted by dark chakra. This immortal might have once been good but something in the past made it turn evil. It now wants to take over the ninja world and use its power to spread darkness.
It could be Orochimaru. Since he has always been obsessed with immortality and power, he might see Naruto's new - found immortality as something he wants to steal or study. He could use his dark jutsus and his army of followers to try and capture Naruto.
It could be an ancient dark ninja who wants to use Naruto's new 'avatar of death' powers for his own evil purposes. This ninja might have been researching death - related jutsus for years and sees Naruto as the key to his ultimate power.
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.