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.
Perhaps an ancient monster that has been awakened by the growing power of chaos. This monster is bent on destroying the world as we know it and Percy has to stop it. It could have unique abilities that make it a formidable foe.
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.
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.
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 a group of mythical creatures that have been experimented on by Shield. They've become more powerful and angry, and they see Percy as a threat. They target him and try to destroy him, as well as causing chaos within Shield. These creatures could be something like mutated centaurs or enhanced harpies.
The Titans could be great antagonists. Even though they were defeated once, they could be making a comeback with new strategies and powers, seeing the Chaos Army as a threat to their plans of regaining dominance. Another option could be the Giants, who are also powerful and have a long - standing grudge against the demigods.
Some of the primordial gods who are jealous of Chaos's newfound relationship with Percy could be antagonists. They might view Percy as an upstart and try to undermine his position. For example, Erebus could try to create chaos in Percy's life in a more malicious way, not in the way that Chaos intends.
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.
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.
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.
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.