Finish off Cyrus
Meet up with Kinzie in Loren Square. Go to the Broken Shillelagh to start this quest. You have to head to Armory Island to find Cyrus. Take a vehicle (or call in a tank or UFO) to get there. You'll be asked to steal a STAG tank. Hijack one (or you can go back to Destructor tank or UFO if you want after doing so) then proceed destroying STAG equipment and other alien forces.
After destroying all marked STAG vehicles, Cyrus will appear. Take out his VTOL then fight him on foot in the helipad. He will be shielded so use your powers to remove it and attack him. He will blink out and call in reinforcements when he reappears but that shouldn't be a problem for you especially if you've upgraded your powers and weapons at this point already.
Super homie Kinzie will now be available. Cyrus will be added as a Homie as well.