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.
It could be a dark demigod who is also seeking the power of the first god but for evil purposes. This demigod might be jealous of Percy's connection to the first god and tries to stop him at every turn.
It could be an ancient and powerful Titan that has risen again. This Titan might have a vendetta against Poseidon and targets Percy as a way to hurt him. Since Percy is Poseidon's son, his death in Poseidon's arms would be a great blow to the sea god.
Maybe there is an old, powerful being who sees Percy's wings as a threat to his rule. This antagonist would try to stop Percy from fully realizing the potential of his wings. For instance, he could set traps or send minions to attack Percy whenever he tries to fly to new places to explore his powers.
It could be a power - hungry Atlantean noble who wants to rule not just Atlantis but also the surface world. He sees Percy as a threat to his plans and tries to stop him at every turn.
A new and powerful demon that has emerged from the darkest corners of the underworld. This demon is bent on using Percy's connection to the overworld to break through the barriers between the two worlds and unleash chaos. It has powers that are different from what Percy has faced before, like the ability to manipulate the very essence of the underworld's environment.
A powerful Amazonian sorceress who has turned against her own kind and is now trying to use dark magic to take over the world. She could see Percy as an obstacle in her path and constantly try to defeat him.
Maybe it could be a demigod who has become obsessed with power through gaming. This demigod, let's say a child of Hades, discovers a way to use dark magic and combine it with gaming technology to try and rule over all the other demigods. He sees Percy as a major threat to his plans because Percy is so popular and has strong powers, so he constantly tries to undermine Percy at every turn.