This is the only creation myth I found, regarding the giant sea serpent (not Leviathan) that appeared in Limsa Lominsa water during 1.0 story.

Legend has it that long, long ago, the world was a parched wasteland, filled with nothing but fire and rocks. Llymlaen, the Navigator, saw this and created a giant serpent to spout forth water and create Eorzea's oceans. But soon she realized that the serpent would never stop, and that all the land would one day disappear beneath the waves, so she sealed the beast away within a floating island called Swallowtail Roam. The island drifts about the sea so that those with evil intentions might never find it...
There's also Midgardsormr's myth, that after Althyk and Nymeia created Silvertear Falls, they charged the wyrm king to protect the waters.