There was never any double jeopardy. Goetz was tried once, and only once, by the State of New York on criminal charges. He was sued by Darrell Cabey, the thug he paralyzed, in civil court.
You may be confusing the fact that the grand jury added attempted murder charges to its original charges after hearing Goetz told the police he said "you don't look so bad, here's another" before taking a second shot at Cabey. That was done pre-trial.
It's also possible you're confusing the fact that the New York Court of Appeals overturned a pre-trial ruling by the criminal court judge, which made Goetz meet a higher burden in his justified use of deadly force defense.
However, there was no double jeopardy.
For some reason I kind of like that quote.