Famous medieval German-Swiss chemist Paracelsus coined this term for female water sprites. An elemental is a mythological being first appearing in the alchemical works of Paracelsus.
In one story an Undine married a human man who vowed to love her with every breath he took, but when he was unfaithful, she cursed him to stop breathing in his sleep and die. He ultimately passed out from sheer exhaustion and suffocated.
After defeating the group of Hydras in Sorrow Valley, the hero can send an Undine to dive into the underground lake to retrieve a mystical jewel that douses the fire wall surrounding Belial's Castle. He'll be prompted three times to ditch the Undine, but if he waits, the Undine will arrive back with the jewel.
"One of the four elemental spirits of Paracelsus, it is a water spirit in the shape of a beautiful virgin. Their name is Latin for "wave." There are tales of some falling in love with humans, and it is said if you marry one, you should never yell at her by water, for she will return there. If you are unfaithful to an Undine, she will kill you."
A Undine once served as one of Skins' demons in Tokyo, Blasted Tokyo, and Infernal Tokyo. She hangs out in the Counter-Demon Force Base in shame at fleeing when he faced the Angels, Pluto, and Kenji, residing there since it reminds her of Skins. Undine is happy that he's still alive when she detects his magnetite on Flynn, leaving after giving him a award for letting her know Skins still lived so that she can go and meet him.