It could be one of Kronos' old allies who feels betrayed that Percy is now in a position of power. Maybe someone who was promised a lot by Kronos but didn't get it.
Another possibility is a demigod who is jealous of Percy's connection to Kronos. This demigod might believe that they deserve that power or heritage more. They could start causing trouble for Percy by turning his friends against him or sabotaging his quests. They would be a more unexpected antagonist compared to the Titans or Kronos' old allies, and their knowledge of the demigod world would make them a tricky enemy for Percy to deal with.
The main antagonist could be a powerful Titan who was imprisoned by Kronos long ago and now wants revenge. They see Percy as an extension of Kronos and target him. This Titan could have unique powers that make them a formidable foe for Percy. For example, they might be able to manipulate time, which would make battles very difficult for Percy as he tries to figure out how to counter such a power.
It could be the Titans who see Percy as a threat. Since he is the son of Kronos, they might want to either use him for their own purposes or eliminate him to prevent any interference in their plans.
A great antagonist could be a Titan who has a grudge against Zeus and sees Percy as an easy target to get back at him. For example, Atlas. He could try to use Percy to free himself from his burden again or trick Percy into doing something that would cause chaos among the gods. Another option is a powerful and vengeful demigod who feels that Percy, as the son of Zeus, has been given too much power and attention, so he wants to take Percy down.
The main antagonist could also be an ancient and powerful spirit from the underworld that was sealed away long ago. Percy's presence as the son of Hades accidentally awakens this spirit. The spirit then starts to spread darkness and despair throughout the world of the demigods, and Percy has to find a way to stop it before it's too late.
A new and powerful Titan who has been hiding and gathering strength all this time. He could be jealous of the Olympians' power and wants to take over. Percy would have to figure out his weaknesses and stop him before he causes too much destruction.
Perhaps an ancient and evil creature that has a grudge against Oin. Since Percy is Oin's son, this creature targets him. It could be a monster that was once defeated by Oin and now wants revenge by going after his son.
Another option could be a corrupted demigod. Maybe a child of a minor Egyptian god who is jealous of Percy's status as Son of Sobek. This demigod could form an alliance with some dark forces and try to undermine Percy at every turn, creating all sorts of challenges for him.
Perhaps an ancient sea god who was once an enemy of Pontus. This god could see Percy as a threat because of his heritage. He would use his own minions, like sea serpents and murlocs, to attack Percy and those he cares about. He might also try to corrupt Percy, tempting him with power to turn against his friends.
It could be a powerful Titan who escaped from Tartarus and wants revenge on Zeus by targeting his son Percy. This Titan might have unique powers that make him a formidable foe.
It could be a new, powerful Titan that has emerged from the depths of Tartarus. This Titan might be seeking revenge on the demigods for imprisoning the other Titans and sees Hylla and Percy as the biggest threats.
A powerful sorcerer from another realm who uses assassins as tools. This sorcerer could see Percy as a threat to their plans of taking over the demigod world. They send their best assassins after Percy and also try to manipulate other demigods against him. They are extremely cunning and have a vast array of dark magic at their disposal.