A Conventional Death
This is a one-time challenge and definitely one of the more challenging ones in the game, due to how quick you need to be to kill Poop Deck before the Skipper does. This can only be done while on the Intelligences of the Artificial Persuasion story mission and is after finishing the events in the engine room.
As already mentioned, you only have a few seconds window from when Poop Deck appears and before the Skipper will slam down the door, killing him. That means you will need to do major damage and quick, so something like a rocket launcher is ideal here. Also, pre-throwing grenades (preferably MIRV ones) at the spot will help.
If you happen to fail in killing him in time, exit the game without saving (quit to the dashboard/XMB on the PS3/360 or simply close the game on PC) and try again.
Hidden throughout Pity's Fall are three special red loot chests.
- This is located on the western side of the map, in the Starboard Ascent area. Right by the Air Dome Generator is a jump pad and to the east of that is a thin fence of sorts. Get on top of thin fence and look south to spot a ledge. Above that is another ledge and you want to boost jump to that one to find the loot chest (there's a vault symbol up here, too).
- This one is located behind an electric barrier in the second to last northern area (the one with all the jump pads). The room with the barrier is on the lower level, but you need to slam a switch. On the western end of the area, at the top, is a fence that you can get on top of (it's thin). Do that and look south to spot a ledge with a button with three green lights, which is the switch for the barrier.
- This one is in the AI Hub room, in plain sight. You won't be able to access this until you get to the end of the Intelligences of the Artificial Persuasion story mission.
This is a one-time challenge and is only possible during the Intelligences of an Artificial Persuasion story mission. When you get to the engine room, you'll have to sabotage it and there will be two things you have to shoot to do this. However, to get this challenge, you have to destroy both of those things without actually shooting them.
The first thing, the flow regulator, appears after setting the engines to full power and is near the ceiling. To destroy this for the challenge, you'll have to jump up to the thing it's connected to and melee it from above until it explodes. After that, you'll use a console and the power stabilizer appears. Simply toss a grenade into the spot where the stabilizer is to destroy that and complete the challenge.
You Call That a Shield?
During the boss battle with the Bosun, you will notice that he has four shield regenerators, which will replenish his shields very quickly. Normally, you would destroy these, but you have to defeat The Bosun without destroying a single one. To complete this the first time around, you're going to need quite the firepower (something like a shotgun will work wonders).
However, considering the Bosun is one of the respawnable bosses in the game, it'll be very easy to come back once you're much more powerful and kill him then.