She is an octopus that has long, stringy hair, (made out of the bottom of a mop) and wears purple jeans and brown boots with heels. She also wears a pink scarf and a blue headband. She wears a yellow top.
After Squidward played the electric clarinet for Patrick (under the guise of a rock star), he didn't change when he rushed back to SpongeBob's house, and so SpongeBob thought he was Hedvig. At first, Squidward was confused but he then caught on, fed SpongeBob trash, and put him outside.