This guide contains spoilers that I have tried to filter out, be warned.
Pit Boss Achievement
Once you get to “The Part Where He Kills You,” Wheatley and PotatOS will have their conversation, and you need to escape Wheatley’s “Mashy Spike Plates.”
Once you do this, start walking down the catwalk, but don’t go to the end. Wheatley will ask you to come back, when he does this, do it. He will then have a bit of dialogue and tell you to jump into the pit. There will be more dialogue convincing you to go down there, so you can listen to that, or just go down.
You will then get the “Pit Boss” achievement!
This one is simple, you will get it by finishing the game. You will also get the companion cube beanie hat with this, so I wouldn’t advise buying it.