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.
Maybe Madara Uchiha, if he were still alive in the fanfiction. He was a powerful and ambitious ninja. He might view Naruto's immortality as a threat to his own plans for the ninja world. He could try to either eliminate Naruto or find a way to use Naruto's immortality to achieve his own goals of creating a world under his control.
It could be Sasuke. If Sasuke has turned completely to the dark side and Naruto fails to save him, Naruto might be so frustrated and angry that it starts to make him cold - hearted towards everyone. Sasuke's actions could be the trigger for Naruto's transformation.
It could be an evil spirit that wants to use Naruto's new ghostly form for its own dark purposes. Maybe it tries to control Naruto and make him do evil things.
It could be Orochimaru. He's always been interested in dark and forbidden jutsus. He might see Naruto as an interesting experiment and use some dark magic on him to turn him into a berserker just to see what chaos he can cause in the ninja world.
It could be Sasuke. If Naruto becomes a wraith, Sasuke might see him as a threat to his own power - seeking goals. Sasuke could try to eliminate Naruto in this new form, thinking that Naruto is now too dangerous or has strayed from the path he believes in.
It could be a new, powerful ninja from a far - off land who wants to destroy Konoha. This ninja might have a grudge against Naruto specifically and forces him to become the shield to protect the village.
Perhaps it's a jealous ninja from another village. This ninja has always been envious of Naruto's power. So when he gets the chance, he uses a dark magic to turn Naruto into a wolf. His goal is to make Naruto weak and lose his status among the ninja community.
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.
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.
Perhaps it's a rogue Shinigami who doesn't want Naruto to figure out how to control his new form. This Shinigami might fear that Naruto could disrupt the balance between Hollows and Shinigami if he becomes too powerful in his hollow state. So, he tries to stop Naruto at every turn, creating a lot of conflict in the fanfiction.
It could be Orochimaru. He has always been interested in experimenting with new forms and powers. If Naruto becomes a monster, Orochimaru might see him as a perfect specimen to study or use for his own evil plans.