Flash Comics #28 its a comic published by DC Comics. It is made of 8 unrelated storylines, each one with a different lead character. In one of those stories we have damsel in distress action.
This happens in the Hawkman story titled The Mechanical Master.
While driving in her car around Hawkman's lair in a mountain, Shiera Sanders is snatched by a giant bird who takes her away, two pigeons witness the kidnapping and go to warn Hawkman about it.
While flying in the claws of the bird, Shiera finds it has a trap door and manages to go in finding out it is mechanical. Inside she finds the creator of the bird and her kidnapper, Karl Mangam who tells her she will be the model for his first mechanical human.
Taken to a house, Shiera finds her duplicate, a model that looks, speaks and even thinks like her, then Mangam takes her away and lets the Hawkman find the fake Shiera. From a hidden spot the girl and the villian watch how the hero falls for the trick and Shiera is broken hearted and further distressed when the villian tells her he will give her a new face so that the hero never recognizes her again.
After getting a new golden hair, Shiera is tied up to a chair and set as a hostage to attract and trap Hawkman. The hero fells for the trap and a heart broken Shiera remains tied up.
However the face change of Mangam proves temporal, Shiera recovers her true face in front of the hero and he is able to escape the trap and then untie the damsel who is fled to safety. Later the villians are stopped and the fake Shiera dissapears.