The Titans could still be a major threat. Even though they were mostly defeated in the original series, some of their followers might see Percy's new role in Atlantis as a threat to their plans for chaos. They could try to undermine Percy's position in Atlantis and use the underwater city as a base for a new uprising.
The Atlantean nobles who oppose Percy's claim to the title of 'Prince of Atlantis' could be antagonists. They might be jealous of the power and influence Percy is starting to gain in Atlantis. They could plot against him, trying to frame him for crimes or start rumors to turn the Atlantean people against him.
The main villain could be a power - hungry Atlantean sorcerer who wants to use the power of Atlantis to rule both the underwater world and the surface. He might see Percy as a threat to his plans and try to eliminate him.
The obvious choice would be the Prince of Darkness himself. He could be a powerful being with the ability to manipulate shadows and dark magic, constantly trying to draw Percy to the dark side.
Obviously, Percy Jackson is one of the main characters. He is the son of Poseidon and has his own set of powers and a strong sense of justice. Another important character could be the current prince or princess of Atlantis. They might be Percy's ally or rival, depending on the story.
The Titans could still be antagonists. In the Percy Jackson universe, they are powerful and malevolent. A princess in a fanfic might have to face their wrath as they try to overthrow the gods and take over the world. They would see the princess as a threat, especially if she is allied with the gods or has some special power that could stop them.
A powerful sorcerer or wizard from within Atlantis who has his own designs on the throne could be an antagonist. This character might see Harry as an obstacle to his own power - hungry plans.
Some of the primordial gods who are jealous of Chaos's newfound relationship with Percy could be antagonists. They might view Percy as an upstart and try to undermine his position. For example, Erebus could try to create chaos in Percy's life in a more malicious way, not in the way that Chaos intends.
It's possible that the main antagonist is a new mythological creature that has the ability to manipulate minds. It has lured Percy and other demigods to the mental hospital and is slowly driving them insane in order to feed off their fear and chaos energy.
The Titans could still be antagonists. They might see Percy as a threat in his new role as the champion of Hecate. Another could be some rogue demigods who are jealous of Percy's new power and want it for themselves. And there could be magical creatures that have been corrupted by dark magic and oppose Percy's efforts to bring balance with Hecate's magic.
There could also be some ancient monsters or spirits that are tied to Olympus' existence. They might rise up to defend it because their own survival is linked to the continued existence of Olympus. These could be powerful beings that Percy has never faced before, adding an extra layer of danger to his quest to destroy Olympus.
Obviously, the God of Death could be a main antagonist if he has some malicious plan. He might be trying to tip the balance of life and death in his favor, causing chaos in the mortal and demigod worlds.