Okay, I did an entry on the Screw Attack Goku vs. Superman Death Battle sometime in the past, but they did a rematch to factor in Super Saiyan God, and Goku apparently lost again.
I actually decided to investigate the claim that Superman can survive the impact of multiple supernovas. Apparently, this isn't true, as Superman only road out the electromagnetic discharge of A SINGLE supernova, and it was stated that the radiation would have killed him. The electromagnetic discharge also did a number on Superman.
This in mind, Goku doesn't need to go Super Saiyan God to kill Superman. Heck, he doesn't even have to go Super Saiyan III. Super Perf