Perhaps a group of rogue demigods who believe that Percy being the first - born of Poseidon gives him too much power and influence. They form a secret society to try and bring him down, using their own unique skills and powers against him.
A powerful Titan who has a grudge against Poseidon could be a great antagonist. This Titan might be trying to undermine Poseidon's power by targeting his first - born, Percy.
A powerful Titan who sees Percy as a threat to his plans. Since Percy has the power of Zeus and Poseidon, he could potentially stop any chaos the Titan wants to create. The Titan might try to turn Percy's friends against him or find a way to strip him of his powers.
A powerful water nymph could be the main antagonist. Maybe she's jealous of the special bond between Percy and Poseidon and the power of the lemon. So she tries to steal the lemon and use its power to take over Poseidon's domain.
Perhaps it could be a new evil force created as a result of Percy's sudden god - born existence. His new - found power could have unbalanced some ancient magic or prophecy, and this new evil entity rises to oppose him and restore the old balance. It might be a being made of dark magic that has a vendetta against Percy for disrupting the natural order of things.
A powerful demigod who has been corrupted by the idea of primordial power could be the main antagonist. They might believe that by allying with a primordial or obtaining their power, they can become greater than the gods. This demigod would then oppose Percy, who stands for the protection of the current order.
An ancient and forgotten god who has been awakened. This god could be angry at the modern demigods for ignoring the old ways and decides to send assassins after Percy as a warning to the rest. They might want to bring back the old order where gods were feared and worshiped more and see Percy as a symbol of the new, more independent demigods.
Perhaps an ancient and dark deity who has been awakened due to some event related to Percy's exile. This deity wants to bring chaos to the world of gods and demigods, and Percy, even in exile, is the only one who can stop it. The deity would use all kinds of dark magic and minions to oppose Percy and his friends.
A new and powerful Titan could be the main antagonist. This Titan could be jealous of Percy's immortality and see it as something that should belong to Titans instead. He could gather a new army of monsters and try to overthrow the Olympian gods once again, with Percy being the biggest obstacle in his way.
A powerful nature - hating Titan who wants to plunge the world into eternal winter could be a great antagonist. He would be directly opposed to Demeter's power over the seasons and crops.
It could be a powerful demigod who was once rejected by the Camp Half - Blood. This demigod, filled with resentment, forms a mafia - like group to seek revenge on those who he believes wronged him. He uses his powers, which could be something like controlling shadows, to create an air of mystery and fear around his mafia operations.
The main antagonist could be a primordial being that has been awakened. It sees the phoenix as a threat to its existence because the phoenix represents rebirth and renewal, which goes against the primordial being's nature of chaos and destruction. So, it tries to destroy the phoenix and Percy has to protect it, along with his friends, using all their skills and the unique powers they possess.