In battle, their attacks will occasionally cause Darkness, but the effect will only last three turns. As with most avian-type fiends in the game, Wakka may be the only character in the party with enough Accuracy to strike it. Lulu can also use Fire magic against it. The Smoke Bombs that can be stolen from them may be used by Rikku for an easy Overkill.
In Greek mythology, Alcyone was the daughter of Aeolus and wife of Ceyx. After the couple insulted Zeus, he killed Ceyx, which caused Alcyone to commit suicide. Out of compassion, the gods then turned Alcyone and Ceyx into halcyon birds.