The Titans who once fought against the gods could also be antagonists. They might view Percy's connection to the Primordials as a way to regain their power and oppose him at every turn. They could send their minions or use their own powers to try and stop Percy from fulfilling his role as the Champion.
Maybe some of the more malevolent Primordials themselves could turn out to be antagonists. If Percy refuses to do their bidding or stands in the way of their plans, they would oppose him. Also, there could be ancient creatures that are awakened by Percy's presence among the Primordials and they see him as an intruder to be eliminated.
The children of Ares might also act as antagonists. They are often at odds with the followers of Aphrodite in the Percy Jackson universe. They might see Percy being the champion of Aphrodite as a threat to their own power and influence. So, they could constantly try to pick fights with Percy, both physically and by trying to turn other demigods against him.
Perhaps some rogue demigods who have turned against the gods and don't believe in Hestia's values. They could be jealous of Percy being chosen as her champion. They might try to undermine his efforts and steal any power or artifacts related to Hestia that Percy is protecting. They could form a sort of anti - Hestia group, causing trouble for Percy at every turn.
One main antagonist could be Nyx, the goddess of the night. Since Apollo represents the sun, Nyx might see Percy as a threat as he is the champion of Apollo. She could try to plunge the world into eternal darkness and send her monstrous children to stop Percy.
Maybe some rogue demigods who are power - hungry. They see Percy's new title as Champion of Ouranos as a way to gain ultimate power. So they would try to either take the title from him or prevent him from using his powers. They could form a secret group and plot against Percy, using their own demigod abilities and knowledge of the demigod world to their advantage.
The obvious antagonists could be the monsters that are constantly trying to thwart Percy's plans. For instance, the Minotaur could make a comeback, being more powerful and cunning this time. It might be under the control of a more powerful force that doesn't want Percy to succeed as Hera's champion.
The Furies could also be major antagonists. They are already powerful and feared in the Underworld, and Percy as the Champion of Erebus might be seen as a threat to their authority. They could try to undermine him at every turn, setting up traps and sending various minions after him. Additionally, there could be a new, unknown force emerging from the darkest parts of Erebus that is opposed to Percy's role. This could be a primordial being that has been awakened by Percy's ascension and wants to return the Underworld to a more chaotic and lawless state.
Maybe Percy has to fight against powerful primordial forces that threaten the world he knows.
The main antagonists could be the Titans who are still resentful of the gods and want to disrupt Demeter's power. Since Demeter is in charge of fertility and the harvest, the Titans might try to cause chaos in that area. Another option could be some dark nature spirits that have been corrupted and oppose Demeter's rule over nature.
Well, there could be some ice - related monsters or creatures that serve Khione. For example, ice giants or frost - breathing serpents. These could be constantly attacking Percy or trying to prevent him from achieving his goals while he's Khione's champion. Also, there might be some jealous demigods who think Percy is getting special treatment from Khione and they become antagonists by trying to sabotage him.