This achievement can be unlocked at the end of Chapter 8, "Search and Rescue".
The progression of the level will bring you to an ADS cannon like the one you used in chapter 4 to shoot down the asteroids.
When you walk into the room with the cannon, turn left and find a save panel on the wall, save your progress before getting into the cannon. That way you can start right back in the room if you fail this portion.
Very similar to Chapter 4's ADS cannon section, your objective is to shoot down things that the slug boss throws at you, as well as shoot all five (5) arms off of it. To do this you want to aim for the glowing yellow spots on the arms. I found it easiest to do when the arm reaches down to pull something off of the ship, as the weak point is stationary for a few seconds. Once all the arms are destroyed you will have successfully killed the slug boss, assuming your shields are still at 50% or greater the achievement should unlock during the following cut scene.
I have included a video to help clarify any confusion, and show how I unlocked this achievement.
**TIPS**
When the arms are trying to or have picked up something to throw at you, shooting the arm causes it to drop whatever it was holding. Use this to your advantage and work back and forth as the arms reach down to prevent them from throwing things at you.
Prioritize any gas tanks the arms throw. These explode when they hit your cannon and do ALOT of damage.
Don't freak out. You start with 100% shields during this section, unlike chapter 4 when you started with 85%, you can take a few hits, so don't let yourself get flustered if your shield drops some.
Be careful not to over heat your Cannon by firing to fast. If you fire both barrels of the cannon at once, the gun overheats very quickly leaving you open to damage. Use one barrel to disrupt the arms, and fire both barrels when you have a clean shot on the weak spots.
This achievement stacks with the "Get off my ship" achievement.
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