Perhaps a sorcerer who has found a way to steal demigod powers. He sets his sights on Percy and Jason because of their unique abilities. He uses illusions and mind - control spells to make them doubt their friendship and themselves. He also creates false threats that lead them on wild goose chases, all while he is preparing to steal their powers when they are at their weakest.
One possible antagonist could be an ancient and powerful Titan who has escaped from Tartarus. This Titan is bent on revenge against the gods and sees Percy and Jason as the key to getting to the Olympians. He uses his dark magic to create all sorts of disasters and tries to turn Percy and Jason against each other. Another could be a group of rogue demigods who have turned to the dark side. They envy Percy and Jason's status and friendship and try to undermine them at every turn.
A sea monster that was once defeated by Percy but has now returned stronger and more vengeful. It teams up with a powerful storm spirit that Jason has angered in the past. Together, they create chaos in the seas and skies, targeting the places where Percy and Jason are most likely to be. They try to separate Percy and Jason by attacking them when they are apart, hoping to defeat them one by one.
Even old enemies of the demigod world, who see Percy and Jason as threats, could be the antagonists. They might use deception and betrayal as a way to weaken the demigod forces, knowing that Percy and Jason are important figures among them.
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.
One antagonist could be Orochimaru from Naruto's world. He could be interested in the power of Quirks in Deku's world and try to capture Deku to study his power. He would be a formidable foe as he is a master of ninjutsu and has a lot of devious plans.
It could be a group of mean girls in their school who are jealous of Bella and Leah's friendship. They try to spread rumors about them, like saying that Leah is only using Bella to get good grades or that Bella is trying to steal Leah's popularity. But Bella and Leah are smart enough to see through their lies and stand up to them together.
The old enemies of Percy and Annabeth like the Titans or some of the more vengeful monsters could be the main antagonists. They might see the unborn child as a threat or an opportunity to get back at Percy and Annabeth.
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.