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.
It could be a former hero who has been turned by the power of chaos. This character would know all of Percy's weaknesses and use them against him. They might have a personal vendetta against Percy and be willing to do whatever it takes to destroy him, even if it means allying with the forces of chaos.
A group of chaos - worshiping mortals could be the antagonists. They believe that chaos is the true form of order and that Percy is an obstacle to their new world order. They use dark magic and chaos - infused weapons to try and take down Percy and his friends.
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.
It might be a new, self - made god. This being has risen from the ashes of human greed and ambition. He sees Percy, the immortal warrior, as a threat to his plans of world domination. He uses his own brand of dark magic and his army of mind - controlled minions to try and defeat Percy. He also tries to turn the other gods against Percy by spreading lies and false prophecies about him.
Perhaps an ancient and malevolent sorcerer who has been awakened from a long slumber. The sorcerer wants to use Percy's powers for his own dark purposes. He sets traps and sends magical creatures to stop Percy as he tries to figure out what the sorcerer is up to and how to defeat him. The sorcerer would be a very tricky antagonist as he can use all kinds of magic that Percy has never faced before.
A powerful Titan who was once a timeless warrior but was banished to the depths of Tartarus could be a great antagonist. He has spent centuries plotting his revenge and now wants to use Percy to break free and destroy the Olympians once and for all.
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 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.