There could be a new, mysterious force that is neither from the Naruto world nor fully part of the Olympian world. This force wants to disrupt the balance between the two worlds and sees Naruto as the key to achieving its goals. It could manipulate both sides and create chaos.
Zeus could be one. He's the king of the gods and has a lot of power. His authoritative and sometimes unpredictable nature might put him at odds with Naruto.
A jealous classmate could be a main antagonist. This person might be envious of Naruto's popularity and his ability to make friends easily. They could try to spread rumors or sabotage Naruto's projects.
The Akatsuki could still be a major antagonist. Even if Naruto is emperor, they might oppose his rule as it goes against their own goals of chaos and obtaining the tailed beasts.
One possible antagonist could be a jealous noble from Naruto's own kingdom who feels that Naruto doesn't deserve the prince title. This person might try to undermine Naruto at every turn, spreading false rumors about him or trying to sabotage his diplomatic efforts.
Another possible antagonist could be a fellow inmate who has a personal vendetta against Naruto. Maybe this inmate was once on the wrong side of Naruto's actions outside the prison and now sees this as an opportunity for revenge. He could try to undermine Naruto at every turn, from spreading false rumors about him to physically attacking him when the guards aren't looking.
Another option could be Orochimaru. He has his own motives and is always looking for power. He could be the head of a powerful gang in the criminal underworld of the Naruto world. He would constantly be trying to capture Naruto or his friends to use them for his experiments or to gain more power over the ninja world.
The Akatsuki could still be the main antagonists. They might be interested in Naruto's tails for their own dark purposes, like using their power to create a super - weapon or gain control over the ninja world. Another option could be a secret group of rogue ninjas who have a vendetta against the Uzumaki clan and see Naruto's tails as a symbol of their power that they want to destroy.
One potential antagonist could be a new and mysterious organization that is similar to Akatsuki but with different motives. They might be interested in using Daisuke to open a portal to a different dimension or something like that. They would be constantly trying to kidnap Daisuke and force him to cooperate. Also, Orochimaru or his remaining followers could be antagonists. Even though Orochimaru has changed somewhat in the series, there could still be some of his followers who are more radical and want to use Daisuke for their dark experiments, believing that he has some special chakra or ability that could help them achieve their twisted goals.
The villagers themselves could be the main antagonists. Since Naruto has been neglected, their continued mistrust and hostility towards him could drive his 'evil' turn. They represent the status quo that has failed Naruto, and he might see them as the source of his problems.
The Akatsuki could still be the main antagonists. Even with Naruto having the power of the Speed Force, they would pose a significant threat. Their various unique abilities and their goal of collecting the tailed beasts would still be in conflict with Naruto's desire to protect the villages.