Definitely the followers of the Olympian gods who are extremely loyal and fear any connection to Kronos. They would consider Percy a walking danger because of his relation to Kronos. Another group could be some of the ancient monsters that were once under Kronos' control. They might sense Percy's connection to Kronos and either try to serve him (which Percy doesn't want) or try to destroy him to sever that link. And there could be some dark demigods who have been corrupted by the idea of Kronos' return and see Percy as a key to that return, but in a way that goes against Percy's own will, so they would try to manipulate him.
The Titans who oppose Kronos' idea of having Percy as his adopted son could be antagonists. They might view Percy as a weak link or a tool that Kronos is using wrongly. So, they would try to either kill Percy or turn him against Kronos. Also, some of the more power - hungry demigods at Camp Half - Blood who see Percy as a rival for power could also be antagonists. They could spread rumors about him and try to undermine his position among the other demigods.
The Olympian gods could be the main antagonists. Since Percy is the adopted son of Kronos, they might see him as a potential threat and try to stop him before he can fulfill any of Kronos' possible plans. They may send their demigod heroes after him.
The Titans could still be antagonists. Even though Percy is now associated with Artemis, the Titans might see him as a threat or a tool to use against the gods. Kronos, for example, could try to turn Percy to his side by offering him power or by threatening those he cares about in Artemis's group.
Another god could be the antagonist. For instance, Hades might be jealous of Demeter's newfound 'son' and the attention Percy is getting. He could send his minions to cause trouble for Percy or try to undermine Demeter's influence on Percy, leading to a series of battles and challenges for Percy to overcome.
The Titans could be antagonists. Since Nyx is an ancient and powerful goddess, the Titans might see Percy as a threat because of his connection to her. They could try to either turn him against Nyx or simply eliminate him.
The Titans who were once associated with Pontus might be antagonists. They could see Percy as a threat to their plans if he is related to Pontus. They might try to stop him from fulfilling any tasks given to him by Pontus or try to use his new identity against him.
Hera could be a main antagonist. Since she's often jealous and protective of Zeus, she might not be happy with Percy being adopted. She could try to undermine him at every turn. Another could be Ares. He might see Percy as a threat, especially if Percy starts to gain more power as Zeus' adopted son.
Some of the traditional sea monsters like the Kraken could be antagonists. Since Percy is now in a more prominent position in the sea world as Amphitrite's adopted son, the Kraken might see him as a threat and try to attack him.
Another possibility could be a group of rogue demigods who are against any form of association with the underworld. They view Percy's new identity as something dark and evil. They form a group to oppose Percy and try to drive him out of the demigod community. They might even try to frame him for crimes he didn't commit in order to get the other demigods to turn against him.
Another possible antagonist could be some of the more power - hungry and jealous demigods. They might not like that Percy has been adopted by Apollo and is getting special attention. They could try to sabotage his missions or spread rumors about him to turn the other demigods against him.
There could also be a group of rogue demigods as antagonists. They might be jealous of Percy's adoption by Hermes and the powers that come with it. They could form a sort of anti - Percy alliance and try to sabotage his quests and make his life difficult among the demigod community.
One possibility could be the old enemies of Hydros. They might see Percy as a threat just because he is Hydros' adopted son. For example, some ancient sea monsters that Hydros defeated long ago could come back to seek revenge on his new family.