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.
Another possibility is a corrupted version of a character from the Naruto world who has been influenced by a negative force related to Apollo. This character could have once been good but now wants to destroy Naruto and everything he stands for because of this new Apollo - related element. They would see Naruto as a threat to their new - found, but evil, power.
Perhaps it's an evil ninja who has somehow harnessed the power of a dark aspect related to Apollo. This antagonist could be trying to use Apollo's power for his own evil purposes, like creating chaos in the Naruto world. He would be in direct opposition to Naruto, who is trying to use Apollo's power for good. So, there would be a battle between the two over the proper use of this power.
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 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.
It could be Hades. He might not like the idea of Percy, a son of Poseidon, being friends with Apollo. Hades could see it as a threat to his own power or plans in the underworld.
It could be someone from the Naruto universe who doesn't like Naruto's newfound fascination with Aku. For example, Danzo might see Naruto's interest in Aku as a threat to the stability of the village and try to stop Naruto from further exploring Aku - related things. So, Danzo could be the main antagonist in this case.
It could be a rogue ninja who also has somehow acquired bankai - like powers. This antagonist might be jealous of Naruto's newfound abilities and wants to prove that he is the stronger one. So he starts causing chaos in the ninja world, challenging Naruto at every turn.
It could be a rogue ninja who wants to disrupt Naruto's business to gain power. Maybe he's jealous of Naruto's success and popularity in the business world. He could try to steal Naruto's business secrets or sabotage his operations.
It could be a rogue Kumo ninja who is jealous of Naruto's power and wants to prove himself by defeating Naruto. This ninja might have some dark secrets and a grudge against Kumo as well.
It could be Orochimaru. He's always been interested in immortality and reanimation techniques. Maybe he reanimates Naruto for some evil purpose, like using Naruto's power to take over the ninja world.
Maybe it's a ninja who has also been affected by Anodite magic but has turned to the dark side. This ninja could be jealous of Naruto's new powers and want to take them for himself. He would use his knowledge of both ninja techniques and Anodite powers to try and defeat Naruto.
It could be a rogue ninja from a rival village. This ninja has a personal vendetta against Konoha and specifically targets Team 10 because of Naruto's presence. He might be jealous of Naruto's growing power and fame and wants to prove himself by defeating the team.