I finally got a device to record PS3 gameplay with, so naturally this was the first project I undertook.
The Big Boss rank can be earned in both New Game and New Game+, and NG+ can make things significantly easier so I wanted to challenge myself and get it done on New Game. I self-imposed other restrictions as well to make things more interesting and I'll go over them here:
As mentioned, New Game, NOT New Game+
No befriending Rebels by giving them recovery items
No using disguises or anything other than the standard Octocamo and Facecamo (in other words not using anything that will make enemies ignore you when you are spotted, and also no using the Metal camo that reduces damage taken by half)
No lethal takedowns on the Beast forms of B&B bosses (I will collect all dolls required to unlock the Solar Gun)
No using psyche recovery items (Syringe is mandatory against Vamp and Screaming Mantis but I won't use it otherwise)
No using Chaff Grenades as they allow you to completely skip many sneaking sections
Must take the longer and more difficult route in Act 3
Must input the correct security code (48273) in Act 4
Must beat Vamp by sneaking up on him

Big Boss Rank Requirements (My stats)

Difficulty: The Boss Extreme (The Boss Extreme)
Total Playtime: 5 hours max. (3 hours 49 minutes 41 seconds)
Saves: Unlimited (9)
Continues: 0 (0)
Alerts: 0 (0)
Kills: 0 (0)
Recovery Items (Rations/Noodles/Regain) used: 0 (0)
Special Items: Restricted (Not used)