You need to kill Gunther with his killphrase. The only way to find out what that is, is to have Jaime Reyes stay at UNATCO. You meet with Jaime after you die in Paul's apartment or if you get captured/surrender to Gunther in Battery Park. After you escape from your cell, ascend as you see fit and find Jaime in his usual spot, the Medical Area in level 3. In the dialogue, make sure you tell him to stay there as a spy.
Later on, as you're progressing during the Paris level, you'll receive a message from Tong, saying that Jaime wants to meet you in a cafe. Go there and talk to him, he'll tell you Gunther's killphrase. Keep progressing through the level. You use it against the German later on, as the boss fight is an unmissable event. Just like Navarre, he doesn't attack on sight, so you can use his killphrase during the dialogue.
The option to use his killphrase in JC's dialogue with Gunther doesn't appear unless you've done the above regarding Jaime.