A new character created specifically for the fanfiction could be the main antagonist. This character could be jealous of the special bond between Naruto and Sasuke. He might have some dark power that he uses to try and drive them apart and prevent them from reaching their full potential in their reincarnated forms.
It could be an entity that represents the dark side of the Naruto and Sasuke's past lives. A sort of manifestation of all the hatred and pain they experienced. This entity tries to pull them back into the cycle of revenge and hatred that they were trying to break free from in their previous lives, and thus becomes the main obstacle for them in the fanfiction.
It could be someone who was also reincarnated from the Naruto universe but with a twisted sense of purpose. Maybe Orochimaru was reincarnated and is now using his knowledge of the past and new - found powers in this new world to cause chaos and try to stop Naruto and Sasuke from reuniting and fulfilling their new destinies.
It could be Orochimaru. He's always had his eyes on Sasuke and Naruto has also been in his crosshairs. He could return with some new and more powerful jutsu, forcing Naruto and Sasuke to put aside their differences and fight him together. Maybe he has a plan to take over the entire ninja world this time.
It could be an old enemy who has resurfaced, like Orochimaru again. Since Naruto and Sasuke are together now, Orochimaru might see them as a threat to his own plans for power and immortality.
It could be a rogue ninja who has a vendetta against Sasuke. This ninja knows that Naruto's bond with Sasuke is strong, so he uses a special jutsu to make Naruto forget Sasuke, hoping to break Sasuke's spirit. By removing Naruto from Sasuke's life in this way, the rogue ninja believes he can defeat Sasuke more easily.
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.