The giant Alcyoneus different than the other giants, he could only be defeated outside of his territory. All the other giants don't work like that, needing a god and demigod together to destroy them. Alcyoneus was made differently then the rest of the giants, and that's why he was defeated.
Alcyoneus couldn't be killed inside his 집 territory, Alaska. So, with the help of Arion, son of Posidon ( Neptune) and Demeter ( Ceres), they managed to drag him out of his 집 territory and kill him. The hero to kill Alcyoneus was Frank, son of Mars ( Ares). He turned into an elephant, charged at him, and thrust his tusks at him.
he was special giant that didnt need a god. he was unable to kill in his 집 teritory (alaska [out of the gods reach])so while percy defeated the ghosts hazel and frank knocked him unconsous and dragged him into canada where they killed him and found percy at a cliff after he dived off the glasier