1540s, "a blow, stroke," from swoop (v.). Meaning "the sudden pouncing of a rapacious bird on its prey" is 1605, from Shakespeare:
Oh, Hell-Kite! All? What, All my pretty Chickens, and their Damme, At one fell swoope? ["Macbeth," IV.iii.219]
sea nymph in the "Odyssey," literally "hidden, hider" (perhaps originally a death goddess) from Greek kalyptein "to cover, conceal," from PIE root *kel- (1) "to cover, conceal, save," which also is the source of English Hell. The type of West Indian song is so called from 1934, but the origin of the name is obscure.
before vowels pyr-, word-forming element form meaning "fire," from Greek pyr (genitive pyros) "fire, funeral fire," also symbolic of terrible things, rages, "rarely as an image of warmth and comfort" [Liddell & Scott], from PIE root *paewr- "fire." Pyriphlegethon, literally "fire-blazing," was one of the rivers of Hell.