* Luke Castellan: Luke is the primary antagonist and the leader of the "bad guys" (the Titan Kronos' army). He's Percy's former friend and counselor at Camp Half-Blood, and his betrayal and manipulation make him a formidable opponent.
* Clarisse La Rue: Clarisse is the daughter of Ares, the god of war, and a fierce, competitive camper. She's always trying to one-up Percy and prove herself as the best warrior, leading to a series of clashes and competitions between them.
* The Furies: These terrifying, vengeful spirits are sent by Hades to capture Percy. Though not exactly a rival, they're certainly opponents Percy has to face.
While there are other characters that might be considered rivals in some ways, such as the monstrous creatures Percy battles or even other campers trying to impress their counselors, these three are the most significant and directly opposed to Percy's goals throughout the book.