Issue #7 (May 1983): The story is titled "This Meeting Will Come to Disorder!" Supergirl battles a giant robot at O'Hare Airport and discovers its origins from a secret underwater complex.
Issue #8 (June 1983): The cover image from your collection is of this issue. It is known as the first appearance of the villain Silver Banshee, in a story titled "The Specter Inside Her!"
Issue #9 (July 1983): Titled "Re-Enter: Reactron", this issue features the New Doom Patrol as guest stars as they team up with Supergirl to fight Reactron, a villain who commands radiation.
Issue #10 (Aug. 1983): Following the battle in #9, Supergirl is suffering from deadly radiation poisoning. In "Radiation-Fever", she is captured for a special experiment by the Organization.
Issue #11 (Sept. 1983): Supergirl manages to escape the Organization's cloning process, but her powers are drained, and she must face off against smaller duplicates of herself in "A Dark and Frozen Purgatory!".
Issue #12 (Oct. 1983): In "Guess Who's About To Die!", Supergirl finds a cure for her radiation poisoning and continues her fight against the duplicates and the Organization.
Issue #13 (Nov. 1983): This is the one-year anniversary issue and is significant for featuring Supergirl in a new costume. The synopsis also involves a storyline where a neighbor of Linda Danvers, a Holocaust survivor, is threatened by a group of fanatics. The title of the story is "Echoes of Times Gone By". The title of the series was shortened to just Supergirl with this issue.