User blog comment:Frodo the 9 fingered/How did they kill Aleconyus?/@comment-98.70.93.13-20111030010031

Nico: "...But Alceonyus, he was different. He was completely immortal - impossible to kill by god or demigod - as long as he was in his home territory."

If he's different, he could probably be killed by anyone as long as he wasn't in the land of his birth - in this case, Alaska. So Hazel was able to shank him into a pile of sparkly rocks without any help.