Well, the Primordial of Destruction is the central antagonist. But it might not be acting alone. There could be some mythical creatures that are under its control, like the Hydra or the Chimera. These creatures would be sent to attack Percy and his friends. Also, there could be a traitor within Percy's own group. Maybe someone who has a personal vendetta against Percy and decides to side with the Primordial of Destruction. This person could leak information about Percy's plans and put him in great danger. And there could be a powerful entity from another dimension that is attracted to the destruction caused by the Primordial and comes to assist it, adding another layer of threat to Percy's mission.
Obviously, the Primordial of Destruction itself would be a major antagonist. It's a powerful and chaotic force that wants to bring about destruction. But also, there could be some demigods who are influenced by the Primordial's power and turn against Percy. They might be jealous of his power or simply be corrupted by the allure of destruction. Another possible antagonist could be an ancient cult that worships the Primordial of Destruction and is trying to bring it back to full power. They would do anything to stop Percy from interfering with their plans.
The Titans could still be a major threat. They might see Percy's new - found power as a way to finally overthrow the gods and use him as a weapon. Kronos, if he were to somehow be resurrected again, would be a formidable antagonist.
Other powerful demigods could be antagonists. They might see Percy as a threat because of his primordial lineage and try to stop him from achieving his goals. Maybe some of them are being influenced by a malevolent god who doesn't want Percy to discover his full potential.
A powerful demigod who has been corrupted by the idea of primordial power could be the main antagonist. They might believe that by allying with a primordial or obtaining their power, they can become greater than the gods. This demigod would then oppose Percy, who stands for the protection of the current order.
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 Titan of Destruction would be the main antagonist. It could be a powerful and terrifying figure, with abilities that can cause mass destruction. It might have a horde of minions that Percy and his friends have to fight through.
Obviously, the Primordial of Monsters itself could be the main antagonist. It has the power and the motive to cause chaos and destruction, which would put it directly in opposition to Percy and his friends.
It could be a new, powerful Titan that has emerged from the depths of Tartarus. This Titan might be jealous of the eldest primordial's power and wants to either destroy it or take its power for itself. And since Percy is associated with the eldest primordial, he becomes the Titan's target as well.
Another antagonist could be a primordial from another realm who is jealous of the power of the primordial of time. This primordial decides to invade the 'Percy Jackson' world and try to absorb the power of the primordial of time. It would bring a whole new level of threat as it has its own set of powers and minions from its own realm. It could also be that this primordial has the ability to twist time in its own realm, and when it enters the 'Percy Jackson' world, it starts causing chaos with time there as well.
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.