It could be the gods. They often have their own agendas and might see the son of chaos as a threat to their power. So they might manipulate Percy into betraying the son of chaos.
Another possibility is a jealous demigod. Maybe someone who is envious of the attention the son of chaos is getting or the power he wields. This demigod could plant false information in Percy's mind, leading to the betrayal.
It could be an ancient evil god who manipulates Percy into betraying the son of chaos. This god might have a long - standing grudge against the son of chaos or his lineage and sees Percy as a useful pawn.
It could be Ares. He might see the Twilight vampires as a new source of power or chaos. He manipulates Percy into believing that the Twilight characters are evil and need to be stopped. So Ares becomes the main antagonist as he's the one driving Percy to betray the Twilight group.
It could be a rogue member of the Hunt. Maybe someone who has a personal vendetta against Percy for some past event or just out of jealousy. This character might be secretly plotting against Percy within the Hunt and is the one who orchestrates the betrayal.
It could be a jealous demigod. Maybe someone who has always been in Percy's shadow and decides to frame him for betraying the gods in order to get rid of him and gain more power and recognition among the demigod community.
Well, it could be that Percy is tricked into believing the son of chaos is a threat when he's actually not. Maybe some other characters manipulate Percy's perception with false evidence.
A powerful chaos deity could be the main antagonist. This deity might see Percy as a threat to their plans of spreading chaos throughout the world. They could constantly send their minions to attack Percy and try to corrupt his mind.
Another possible antagonist could be a rogue demigod who is corrupted by the power of Chaos. This demigod might envy Percy's connection to Chaos and decide to turn against him. He could form his own group of followers, causing chaos (literally) in the demigod world. They would oppose Percy and his friends at every turn, believing that they are the rightful heirs to the power of Chaos.
A powerful primordial being awakened from the depths of Chaos could be a great antagonist. This being could have powers that surpass even the Olympian gods and a desire to reshape the world in its own chaotic image.
It could be an ancient and powerful Titan who has escaped from Tartarus. This Titan wants to use Lady Chaos's power to take over the world. He sees Percy as a threat because of his past victories against the Titans and his connection to Lady Chaos.
There's a chance that it could be a character from Percy's family. For example, a distant relative who has been corrupted by some dark magic. They might betray Percy for their own gain or because they are being controlled, and this betrayal could lead to Percy being killed.