A powerful demon or dark spirit could be the main antagonist. This entity could be attracted to the combined power of Naruto and fem Apollo. It might seek to drain their powers to become even more powerful itself. For example, it could be a demon from Naruto's world that has somehow crossed over into Apollo's realm and is causing chaos there, targeting both Naruto and fem Apollo because they pose a threat to its plans.
It could be a dark figure from Greek mythology who wants to stop Naruto from fulfilling Apollo's will. Maybe a Titan who is jealous of Naruto's new - found connection to Apollo.
It could be an ancient evil spirit that was sealed away by Fem Hashirama in the past. Now that she has resurfaced in the Naruto - era, the spirit is also awakened. This spirit wants to destroy the world that Fem Hashirama once protected and Naruto, being the hero of his time, stands in its way along with Fem Hashirama.
It could be Orochimaru. He's always been interested in unique powers and abilities. The idea of X - 23's mutant abilities and Naruto's jinchuriki powers would be very appealing to him. He might try to capture them both to use in his experiments to gain ultimate power.
It could be an old enemy of the gods, like Kronos. Even though he was defeated before, he could find a way to come back and target Percy and Apollo specifically. Since Percy has been a thorn in the side of many of the Titans' plans before, and Apollo is a powerful god, Kronos might see them as a threat to his new - found or potential power.
One possible plot could be that Naruto, through some sort of magical or dimensional rift, ends up in a world where Apollo exists as a female. Naruto, with his determination and kind heart, befriends fem Apollo. They could go on adventures together, Naruto teaching her about his ninja world and she in turn sharing her knowledge of her own realm. Maybe they have to team up to fight a common enemy that threatens both their worlds.
Maybe an evil sorcerer from a third, unknown dimension who sees the potential in both Naruto's chakra and Pneuma's power. He plans to steal their powers to become invincible. He starts by creating unrest in both their worlds, pitting their friends and allies against them. Naruto and Pneuma must figure out his true identity and stop him before he succeeds in his devious plan.
It could be an evil ninja who has somehow gained access to the technology from Neo's world and wants to use it to take over the Naruto world. He might be able to create clones using digital technology, making him a very difficult enemy to defeat.
It could be a rogue member of Kara who has their own agenda and doesn't agree with any form of alliance with Naruto or the Hidden Leaf. This character might try to undermine any cooperation between Naruto and the rest of Kara.
Madara Uchiha could be a great antagonist. He could have somehow gained the power to cross into the Bleach universe and is causing trouble there. Yoruichi and Naruto would have to put aside their differences and combine their skills to stop him. Madara's powerful jutsu and his desire for power would make him a formidable foe for the duo.
It could be an organization of dark summoners. They believe that by sacrificing Matatabi, they can gain ultimate power. They send out their best agents to hunt down Matatabi and Naruto. These agents have the ability to manipulate dark chakra, which is harmful to both Naruto and Matatabi. The organization's leader is a powerful sorcerer who has been planning this for years.