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.
Maybe a powerful and corrupt demigod. This demigod has become power - hungry and believes that by controlling Lady Chaos, he can rule over all demigods and gods. He sets out to stop Percy from getting too close to Lady Chaos and tries to turn the other demigods against Percy.
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.
The Titans could still be a major threat. Even if Lady Styx is involved, the Titans might see an opportunity to use the chaos she causes to their advantage. For example, Kronos could try to ally with Lady Styx to regain his power and overthrow the Olympians once again.
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.