Maybe it's a corrupted god. Let's say Hades in this case. He's always been a bit of an outcast among the gods. He decides to use Percy as a test subject in a plot to gain more power in the underworld. He subjects Percy to all sorts of trials and tests that are meant to break him down and extract his power. Percy has to fight against Hades' dark magic and find a way to escape his clutches.
The main antagonist could be an ancient and powerful magic being that has been awakened from a long slumber. This being views Percy as a unique specimen because of his demigod status. It wants to study Percy's reaction to different types of magic and use the knowledge to take over the world of the gods and demigods. It sets up elaborate traps and challenges for Percy, constantly pushing him to his limits.
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.
The goddess Hera might also be a great antagonist. Since she has a history of interfering in the lives of demigods, she could be jealous or threatened by Percy's rebirth. She might try to stop him from reaching his full potential in his new life or cause trouble between him and his new allies.
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.