Meet the Crew to Bring Down Zinyak
Go to Kinzie's warehouse in Salander to start this quest. Enemy troops will start flooding in the warehouse. Your power will be gone so you'll have to rely on your default weapons. A fully upgraded Singularity Gun is perfect for this situation. Clear out the warehouse until you get the objective to move on. Destroy the tanks outside the warehouse as well as any heavy hardware the enemy may have. Continue to the rooftop to find a helicopter.
Use the helicopter to protect the allied car below. It can fire homing rockets and a heavy machine gun. You don't have to destroy everything; you just need to concentrate in taking out the immediate threats and blockades on the road. After a while you'll have to scout ahead and discover two tanks blocking the main path. Take them out and continue escorting your allies until you reach the next area of the city. Here your chopper will be shot down and you'll have to take refuge inside the building. Take the elevator.
Once inside the Genkibowl building, take out the first wave of zin troops while protecting Kinzie. The quest will be updated after a while and you'll have to build up the murder meter. Keep killing enemy troops until Prof. Genki shows up. Take him out as well to complete this section.
On your way out, you'll have to use your RPG to take protect the vehicle. Keep shooting at your pursuers and take out the blockade. Zinyak himself will appear, taking Kinzie with him.
You'll wake up in the ship. Check up Kinzie's unconscious body and stand by the door to wait for the zin forces that will break it. Take them out and proceed to the lower deck. Clear out the floor and proceed to the bridge next.
After learning your current situation, head to the cargo bay. Take out more enemies and help Shaundi. Clear out the cargo bay and discover that the zin has planted some explosives. Pick the explosives up and head to the airlock.
Continue killing more enemies until you get a heavy weapon. Use it to continue clearing the pathways until you reach the alien ship's reactor. Plant the first explosive there.
Follow Gat and fight your way through more enemy resistance until you reach the controls. Plant the second bomb there and make your way out. Follow Gat and ignore the enemies along the way. After reaching the airlock, a zin trooper will grab you. Press RT to kick him and escape. The quest will be complete after a few scenes.