Antaeus

Antaeus was a giant of Libya, the son of Poseidon and Gaia, whose wife was Tinjis.

History
He was extremely strong as long as he remained in contact with the ground (his mother earth), but once lifted into the air he became as weak as other men. He would challenge all passers-by to wrestling matches, kill them, and collect their skulls, so that he might one day build out of them a temple to his father Poseidon. Hercules, finding that he could not beat Antaeus by throwing him to the ground, as he would regain his strength and be fortified, discovered the secret of his power (touching the ground) and held Antaeus aloft and crushed him in a bearhug.

The series
Antaeus is the ruler of an arena, and Percy is given up as a warrior. He first fights a collection of monsters, then the demigod Ethan Nakamura. Then Percy challenges him to a fight, and Annabeth tells him that he is a son of Gaia, and when Percy sees he cannot kill him, he deduced that as long as he touched the Earth, Gaia kept him alive. So Percy wrapped a chain around Antaeus, and lifted him in the air, and then stabbed him.

Species
As Antaeus was the son of Poseidon and Gaia, he was a god, and should not have been able to be killed at all.