Some of the Titans who still hold grudges against the Olympians might see Percy's rise to king as an opportunity to create chaos. They could try to manipulate Percy or turn the other gods against him. There could also be new, original villains created specifically for the fanfic. Maybe a powerful demigod who is jealous of Percy's status and wants the throne for himself. This demigod could have some dark powers or be in league with dark forces that help him in his quest to stop Percy from becoming king.
Another possible antagonist could be an ancient and powerful monster that has been awakened by the news of Percy's potential kingship. This monster could be seeking revenge on the gods and sees Percy as a symbol of their power. It could attack Percy and his friends, trying to prevent him from ascending to the throne and bringing a new era of peace and order to the world of the demigods.
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.
A group of hunters who have a vendetta against wolves could also be antagonists. They might be descendants of some ancient hunters who were cursed by a god to always hunt wolves. Percy, as the king of wolves, has to protect his pack from them.
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.
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.
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 Titans could still be antagonists. In the Percy Jackson universe, they are powerful and malevolent. A princess in a fanfic might have to face their wrath as they try to overthrow the gods and take over the world. They would see the princess as a threat, especially if she is allied with the gods or has some special power that could stop them.
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.
The Titans could still be a major threat. They might see the Beast King as a new power to either control or destroy, and they would oppose Percy's attempts to make peace with the beast kingdom.
The old - guard Olympians could be the main antagonists. They might see Percy as a threat now that he's the King of the Titans. They're used to being in power and might not want to share or give up any of their influence.
Some of the more traditional Spartan nobles could be antagonists. They don't like the idea of an outsider like Percy being king. They might plot to overthrow him and restore the old Spartan monarchy without his more modern and demigod - influenced ideas. They could use their influence over the military and the common people to try and get rid of Percy.
It could be a group of rogue demigods who want to use the Dragon King's power for their own evil purposes. They might be jealous of Percy's status and see the Dragon King as a means to gain more power and control in the mythical world.