Superman/Supergirl Maelstrom was a 5 part mini-series spanning from November, 2008 to March, 2009. 
 
The series began with the introduction of a Apokoliptian woman called Maelstrom who desired very greatly to "...be the new bride of Apokolips." She planned to win Darkseid's affections by bringing him the head of Superman, which led her to travel to Earth where she battled and defeated Supergirl. The effect of this defeat carries into the rest of the issues, resulting in Superman and Supergirl training on an alien planet under a red sun to hone their skills while Maelstrom, escorted by the Female Furies, prepares for a final battle with Superman.