Maybe it's a magical creature that has the power to manipulate Annabeth's mind. It makes her tie up Percy so that it can carry out its evil plan without Percy interfering. In this case, the magical creature is the antagonist.
It could be a new demigod who has a grudge against Percy and somehow convinces Annabeth that Percy is a threat, leading to her tying him up. So this new demigod would be the antagonist.
There's a chance that it's a rival group of demigods. They trick Annabeth into believing Percy has betrayed their side and get her to tie him up. So this rival group would be the antagonists in the story.
Maybe the main antagonist is an old enemy of Percy's who has learned about his newfound ability to hypnotize (even if it was accidental). This enemy decides to use Annabeth as a pawn by hypnotizing her, hoping to lure Percy into a trap and defeat him once and for all.
It could be a jealous demigod. Maybe someone who has always been envious of Percy and Annabeth's relationship and popularity. This person finds a way to manipulate some dark magic or an old rule to force them into marriage, hoping to create chaos in their lives.
It could be an ancient and powerful god or goddess who has a grudge against Percy. Maybe they see Percy as a threat to their power or plans, so they plot his death. For example, a forgotten deity who wants to regain their former glory by getting rid of Percy, who is often seen as a hero in the Percy Jackson universe.
One possibility could be that it's part of a prank gone wrong. Maybe Annabeth was trying to play a practical joke on Percy and tied him up, but then things start to spiral as they face some unexpected danger while he's tied. And they have to figure out how to get Percy free and deal with the situation together.
It could be Percy himself if he's acting unjustly. Even though he's beating up Hercules, if his reasons are not noble, like if he's just being full of hubris, then he would be the antagonist.
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It could be Chiron, the centaur. He's always keeping an eye on the campers and would likely be concerned if he caught them up to something. He might give them a stern talking - to and some extra chores as punishment.
A group of rogue demigods could be the main antagonists. They might be jealous of the attention the daughter gets because of her parents. So, they plot to make her life difficult and try to drive a wedge between her and the other demigods.
The main antagonist might be an ancient and powerful being that has awakened. This being could see Percy and Annabeth as a potential threat to its plans of taking over the demigod world. So, it uses its influence to have them banished, thinking that without them, it would be easier to conquer. For example, a long - forgotten Titan who has found a way to break free from its prison.
It could be an old enemy of Percy and Annabeth. Maybe a monster that they thought they had defeated long ago but has come back for revenge. This time, it might target Annabeth's daughter to get back at them.