Sirena del baile, according to BabelFish. My caller was doubtful, but it sounded right to me. Googling the phrase gets me a couple of Spanish-language hits for Esther Williams.
The Sirens, against whom Ulysses lashed himself to the mast, wishing to hear their song without being lured to his death.
The translation is problematic because, as John William Waterhouse has correctly painted them here, the Sirens were bird-women, not fish-women. But the Spaniards call mermaids sirens, and that's that.
Tiny purple fishes...