Aliens plot to conquer the world using mind-controlling sunglasses in Adventure 423 (Sept 72), a story by E Nelson Bridwell and Steve Skeates, with art by Mike Sekowsky and Bob Oskner.
Linda is out shopping when a pushy saleswoman shoves a pair of sunglasses on her, and she discovers she cannot remove them. The glasses also force her, or anyone wearing them, to follow the commands of the aliens who created them.
She is ordered to Metropolis, where she switches the glasses with Clark Kent’s usual ones, rendering him under the aliens control as well.
The two aliens brothers behind this are not working together well, and one decides to betray the other, and has Supergirl use her heat vision, which results in the destruction of the glasses, freeing her mind.
Superman brings the glasses to the Justice League, but Supergirl intervenes, much like the scene on the cover, and gets Green Lantern to destroy the glasses Superman is wearing.
A fairly silly story. She still has her problems with her powers vanishing at times in this tale, although that has been used less frequently in recent months, and this would be the last story to reference that.