It could also be that the Olympian Council as a whole acts as the antagonist. They might have made decisions that Percy sees as a betrayal, such as sacrificing the safety of demigods for their own political gain. Each god on the council, with their own self - interests, might contribute to Percy's feeling of betrayal, making the council as a whole the main force he has to oppose.
The main antagonists would most likely be the gods themselves. Since the title mentions being hunted by the gods, they would be the ones sending various threats Percy's way. It could be Zeus, who is often quick to anger and punish those he thinks are a threat to his power.
The traditional gods who don't want to see Percy as king could be antagonists. For example, Zeus might see Percy as a threat to his power and try to stop him at every turn.
Other jealous demigods could act as antagonists. They might feel that Percy doesn't deserve the blessings and try to undermine him. They could spread rumors or even try to sabotage his quests to make him look bad in the eyes of the gods.
The Giants might also be antagonists. They could band together and target Percy's kingdom, believing that by destroying him and his rule, they can undermine the power of the gods further. They might use their brute strength and strategic thinking to attack Percy from different fronts.
Another option could be a group of rogue demigods who have turned to the dark side. They follow Percy to Forks, hoping to find some powerful artifacts there. They don't care about the vampires or werewolves and are willing to cause destruction to get what they want. Percy has to stop them while also dealing with the local supernatural creatures.
Obviously, the gods themselves would be the main antagonists. They have the power to manipulate Naruto's world and his fate. They could be some sort of ancient deities who have been watching over the ninja world from afar and now feel the need to interfere.
The Titans could be the main antagonists. Even though they have been defeated before, some of them might have found a way to return or their followers could be causing trouble. They see Artemis as a threat or a target for their revenge against the gods. Another possibility is a new group of powerful monsters that have banded together and are specifically targeting Artemis for her power and influence among the demigods.
Well, the main antagonists could be a group of rogue demigods who have formed a cult around Kronos. They believe that Percy, as the heir of Kronos, should lead them in overthrowing the current order of the demigod world. But Percy doesn't want any part of it, so they become his enemies. Another possible antagonist could be an ancient being that was once in league with Kronos and now sees Percy as a means to resurrect Kronos or continue his dark legacy. This being would stop at nothing to force Percy to embrace his role as the heir.
Perhaps some of the older, more traditional gods could be antagonists. They might see Percy as a threat because he's now the God of Dinosaurs and they fear the power he could gain from controlling these ancient and powerful creatures. For example, Zeus might be worried that Percy's new role could disrupt the existing power balance among the gods.
The Roman gods could be antagonists. Since Percy is a Greek demigod, they might not fully trust him as the King of Rome. They could try to undermine his rule, believing that he will favor the Greek side in any disputes or decisions regarding the demigod world.