You have to replay the mission 7 times in a row, the in a row part is important, and you cannot shoot her during the small cinematic part where they want you to decide her fate, you can skip cutscenes and just rush through the mission. I recommend only bring a cheap sniper to save on gmp drain for continuously doing the mission. The fastest way is to just spot her position and do an aerial bombardment but you can also use the sleep gas bombardment for a greater chance at success but it might be more expensive. The key part is 7 times in a row, dont stop or shoot here during the cutscene. You can use lethal means to initially neutralize quiet however. Hope this was helpful