There might be some ancient chaotic creatures that Percy has to target as an assassin. However, these creatures could be intelligent and fight back, making them the main antagonists. They could also have their own motives and reasons for causing chaos, which might make Percy question whether he is doing the right thing by trying to assassinate them.
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.
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.
Well, perhaps Percy starts off as an ordinary character but gets drawn into the chaos realm. He could be forced to become an assassin due to some threat to his friends or family. Maybe he discovers new powers that make him suitable for this role.
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.
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.
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.
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.
It could be some of the other trainees who are jealous of Percy's progress and his special relationship with Chaos.