Supergirl deals with a magical monster that almost exposes her identity in this Cary Bates story from Adventure 386 (Nov 69)
The mysterious beast seems to have a crush on Supergirl, and follows her around. Only she can get it to obey, and even then only briefly.
It shows up at a dance at Stanhope College, and tears off Supergirl’s Linda Danvers guise, but as it’s a costume ball, and another student was hiding a Superman outfit under his costume, Linda gets away with the situation – although no one seems to notice that she lost the brown wig she wears as Linda – the blonde hair of Supergirl is clearly her real hair.
She brings the creature to the Fortress of Solitude, where she causes it to say kltpzyxm, which reveals the creature as Mr Mxyzptlk, and sends him back to his dimension.
Her logic, when she explains her deduction to Superman, leaves much to be desired. The creature could easily have been a magical creature, there was nothing to prove it HAD to be Mxyzptlk. But this story clearly didn’t care too strongly about logic gaps, after the wig situation.