The main antagonists could be a rival clan of monsters that wants to overthrow the Monster King. They see Naruto as an interference and try to get rid of him while also plotting against the Monster King. Naruto then has to help the Monster King defend his throne and protect the balance between the two worlds.
It could be a group of rogue ninjas who want to use the power of the Monster King for their own evil purposes. They might try to capture the Monster King and force it to do their bidding, which would put them in direct conflict with Naruto.
Perhaps there is an ancient curse that turns some of the monsters into uncontrollable beasts. These cursed monsters could be the main antagonists as Naruto and the Monster King have to work together to find a way to break the curse. And there might be a shadowy figure behind the curse, pulling the strings.
Maybe the Hidden Leaf Village elders could turn into antagonists. They might fear Naruto's new power as the demon king and try to undermine him. They could form alliances with other villages to try and take down Naruto. Also, there could be some new, unknown powerful forces that emerge because of Naruto's transformation. These could be ancient evils that were once sealed away but are now awakened by Naruto's new demonic presence.
It could be the Akatsuki. Even though Itachi was once part of them, now that he has the power of a Jinchuriki, they might see him as a threat. They could want to capture him to either extract the tailed beast or to stop him from using its power against them.
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.
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.