Maybe there is a shadowy organization that is against the existence of Percy's secret life. They view it as a threat to their own plans and will stop at nothing to eliminate Percy and his secret world.
It could be the navy. They see pirates as outlaws and would be determined to capture Percy and his crew. They might have better - equipped ships and more trained soldiers, making them a formidable foe for Percy and his fellow pirates.
Monsters could also be antagonists. With Percy in a new, more powerful state as a godling, there could be new and more powerful monsters that are drawn to his power. These monsters might be stronger and more intelligent than the ones he faced as a demigod, and they could be after his godly essence or trying to use him for their own dark purposes.
A powerful sorcerer who wants to use Percy for his own dark purposes could be an antagonist. This sorcerer might see Percy's unique abilities as a key to unlocking some sort of forbidden magic.
There could be some traditionalist ninja in the village who oppose Naruto because she's a girl trying to break the norms. They might see her as a threat to the traditional male - dominated ninja culture and try to stop her from achieving her dreams and rising in the ranks of the ninja world.
The Titans could still be antagonists. Even though Percy is raised by Chaos, the Titans might see him as a threat to their plans of overthrowing the Olympians. They could try to capture or kill him to prevent him from interfering.
The other gods who are jealous of Percy's new connection with Hades could be antagonists. For example, Zeus might see Percy as a threat now that he has Hades' blessing.
The old - fashioned and conservative gods who don't like the idea of a new, young god like Percy shaking up their established order could be antagonists. They might see him as a threat to their power and try to undermine him.
In this kind of fanfiction, the Titans could also be antagonists. They might want to use Percy's power over time to their advantage. Maybe they think they can rewrite history in a way that would bring them back to power. Kronos, in particular, if he were somehow still a threat, could be a major adversary. He could try to manipulate Percy into using his time powers in a way that would benefit the Titans, like going back and changing events that led to their downfall.
The main antagonists could be some of the more traditional and power - hungry gods. For example, Hera might see Percy as a threat to the order she has maintained for so long. She could try to undermine him at every turn, fearing that his new ideas and his relation to Zeus will disrupt her plans. Another antagonist could be Ares, who might be jealous of Percy's potential power and influence over the other gods and demigods.
The Titans who once fought against the gods could also be antagonists. They might view Percy's connection to the Primordials as a way to regain their power and oppose him at every turn. They could send their minions or use their own powers to try and stop Percy from fulfilling his role as the Champion.