The gods themselves could be antagonists in a sense. They might be worried about Percy's powers getting out of control. So they could try to limit his freedom or even try to get rid of him. Zeus, in particular, might be very suspicious of Percy and constantly keep an eye on him. This could create a lot of tension between Percy and the gods, and Percy would have to find a way to prove himself and deal with their interference while also facing other external threats.
The Titans could be great antagonists. They might see Percy as a threat to their plans of overthrowing the gods again. Since Percy has chaos powers, they could fear that he could disrupt their carefully laid - out schemes. Another possibility is some of the more traditional enemies of the demigods, like the monsters. They might be drawn to Percy's chaotic energy and try to either consume it or destroy him to prevent him from becoming too powerful.
Perhaps Percy could be in a constant battle within himself. On one side, his normal demigod self with loyalty to his friends and Camp Half - Blood, and on the other, the chaotic side of him that wants to disrupt and change things. He might meet other 'children of chaos' and they could either be his allies or enemies. And his journey could involve learning about the true nature of chaos and how to use his powers for good, like protecting the world from a greater chaos that threatens to engulf it all.
It could be the entities that thrive on the disorder in the chaos. They might see Percy and Bianca as threats to their way of life and try to stop them from achieving whatever goal they have in the chaos.
It could be the agents of Order who see Percy and Thalia joining Chaos as a threat to the balance they strive to maintain. They might send their best warriors to stop Percy and Thalia from carrying out Chaos' plans.
The Titans could still be antagonists. Even though Percy is raised by Chaos, the Titans might see him as a threat to their plans of overthrowing the Olympians. They could try to capture or kill him to prevent him from interfering.
A likely main antagonist could be a powerful demigod who has turned to the dark side and wants to use chaos for his own evil purposes. He might see Percy as a threat to his plans.
Another vampire, an older and more powerful one, could be an antagonist. This vampire might see Percy as a threat to his power or territory. Maybe he wants to either kill Percy or make him submit to his rule.
The old - fashioned and conservative gods who don't like the idea of a new, young god like Percy shaking up their established order could be antagonists. They might see him as a threat to their power and try to undermine him.
The Titans could still be a major threat. Since Percy is now the Host of Chaos, they might see him as a new opportunity to regain power. Kronos could try to manipulate Percy's chaotic powers for his own gain, or maybe use Percy's new status to cause more chaos in the world and then step in to 'restore order' in a way that benefits the Titans.
It could be the Titans or some new creatures that are jealous of Percy's connection to Chaos. They might see Percy as a threat and try to stop him and Perlia from achieving their goals.
Maybe the gods or powerful beings who are trying to maintain the current balance and see Percy's new role as a disruption. They would try to stop him from carrying out his assassinations in the chaos world.