This isn't so much a guide on how to get the achievement (as it's quite obvious how to go about doing side quests, romancing and loyalty missions once you enter virtual Steelport), it's just a heads up that Kinzie's last quest won't be available until you complete the Hello Teacup story mission which unlocks the
Poodle Skirt achievement.
I thought this one had glitched on me as I had done all the available quests and had earned the similar achievements for all the other characters. As soon as I completed the above mission, a final quest for Kinzie appeared.