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 Battle of the Labyrinth
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.

Debatable Species
Some say as Antaeus was the son of Poseidon and Gaia, he was a god, and should not have been able to be killed at all, calling this instance a 'mistake' in the series. Others claim that since Antaeus was killed in the actual myth by Hercules that he lost some of his immortality, which in turn could be associated with his death at the hands of Percy Jackson. This is highly debatable and without comment from the author, will remain unclear. Monsters in the series disintegrate into dust after being fataly wounded, gods on the other hand simply explode into unbearably bright light after wounds, and can almost always teleport as a side ability. The way Antaeus died was a very unique way, and apparently, even though he died in the myth he still resurrected to fight Jackson, (a characteristic commonly used to explain monsters) his position is unknown.