It could also be an ancient, evil force that has been awakened by the curse. This force might have been sealed away long ago by the gods, but the curse on Percy somehow breaks the seal. The force then starts to target Percy, seeing him as the key to its full resurrection. It would use all kinds of dark magic and minions to try and capture Percy and use his power, which has been distorted by the curse, to break free completely from its prison.
The main antagonist could be one of the major gods who cursed Percy. For example, Zeus might be angry with Percy for some reason and decide to curse him. Zeus would then use his power to send all kinds of obstacles and enemies Percy's way. He could manipulate the weather to create storms that target Percy or send powerful monsters after him.
The gods themselves could be the main antagonists. Since they cursed Percy, they might be trying to keep him in a state of misery or use him for their own purposes.
It could be an envious demigod who feels that Percy doesn't deserve his new position as a consort of the gods. This demigod might plot against Percy, trying to undermine his influence among the gods and the other demigods.
A group of rogue demigods who have turned against the gods and see Percy as a traitor for being so close to them. They form an alliance and try to stop Percy from fulfilling any quests or tasks given to him by the gods, and might even try to capture or kill him.
Set, the Egyptian god of chaos. He could be a great antagonist as he might see the combination of Greek and Egyptian powers in Percy and the other demigods as a threat to his own plans of spreading chaos. He could try to manipulate events to turn the two groups against each other.
Another possibility is a demigod who has turned against the other demigods and sided with a particularly cruel god. This demigod could have been corrupted by power or a desire for revenge, and they use their knowledge of the demigod world to help the god in the war. Percy would then have to face this former ally, which would be a very emotional and difficult conflict for him.
The main antagonist might be a new character, a powerful being that rules the realm where Percy is banished. This being could see Percy as a threat to his or her power and try to stop Percy from finding a way back.
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.