It could be a group of rogue spirits from the Chaos itself. These spirits have no form but can possess people and objects. They are drawn to the power that Percy might have as the Prince of Chaos and want to use him to break free from the boundaries that keep them in the Chaos. They start causing chaos in the mortal and demigod worlds, and Percy has to find a way to stop them without being completely taken over by their influence.
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.
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.
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.
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.
It could be an ancient and powerful being from the chaos realm who sees Percy and Piper as intruders and a threat to its own power. This being might have been ruling over a certain part of Chaos for eons and doesn't want the demigods to disrupt the status quo.
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 a power - hungry Atlantean noble who wants to rule not just Atlantis but also the surface world. He sees Percy as a threat to his plans and tries to stop him at every turn.
A new and powerful demon that has emerged from the darkest corners of the underworld. This demon is bent on using Percy's connection to the overworld to break through the barriers between the two worlds and unleash chaos. It has powers that are different from what Percy has faced before, like the ability to manipulate the very essence of the underworld's environment.
A powerful Amazonian sorceress who has turned against her own kind and is now trying to use dark magic to take over the world. She could see Percy as an obstacle in her path and constantly try to defeat him.
Maybe it could be a demigod who has become obsessed with power through gaming. This demigod, let's say a child of Hades, discovers a way to use dark magic and combine it with gaming technology to try and rule over all the other demigods. He sees Percy as a major threat to his plans because Percy is so popular and has strong powers, so he constantly tries to undermine Percy at every turn.