Brunhilde is a flight attendant for Budget Airways, encountered in the 1983 storybook The Muppets on the Road. She hires the Muppets to perform at the airline's upcoming show, then bundles them into a plane and hands them all parachutes. It turns out that the "entertainment" is an air show, and the group is hurled off the plane to drift to the ground. She neglects to give the gang their promised payment of $38.47 before they jump.
The character's name is likely a reference to Brünnhilde, a character in Richard Wagner's opera Die Walküre.