Well, you’ve rescued Matt Miller from his simulation, but his real body is still stuck on Zinyak’s ship. To help with this endeavor, Kinzie gives you some "power armor," although it’s really just a mech. Should your mech get damaged, you’ll be able to find health in blue crates. You have to resort to melee attacks, since Kinzie couldn’t get weapons onto the mech.
When you begin the mission and get to the first door, you find that you can’t fit through it and will need to use your thrusters to get to the top of the room. The next door can be destroyed by either your shoulder bash attack or a melee one, so use either and go through it. Hover over to the platform with the enemies and kill them, then smash through the door and kill some more.
In the next area, you’ll have to propel yourself over two gaps, so make sure you stop in between to let your thrusters recharge. Keep going through the areas, killing the Zin in the way, until you eventually find Matt. He will follow you and help out with the mech’s lack of weapons, so you’ll need to protect him from the incoming Zin while he finds some parts to make your mech into the killing machine it deserves to be.
Try to stick close to Matt, so you don’t have to worry about traveling far to protect him should the Zin get to him. Clean up the rest and you will receive your shiny new weapons, rockets and a mini-gun. Note that the rockets can overheat, so be careful with those (the mini-gun should be more than enough for most enemies to come).
It should be easier to fight through the Zin now and you’ll come to a big area where you’ll have to fight off a lot of waves of Zin, some of which will include Murderbots and enemy ships now. Eventually, the weapons on your mech will malfunction, meaning you’ll have to clean up the rest of the enemies with your melee abilities.
With all of the enemies now dead, make your way to the marker and you’ll be back on the ship. Unlike last time, you’ll be manning the turret and will have to shoot down any ships coming after you. Eventually, one of the battleships (remember when the Zin first invaded) will be coming after you, but you won’t be able to do any damage to it, so ignore it. At the end, listen to Kinzie and shoot the right panel to finish the mission.