Boss: Psycho Mantis
Game: Metal Gear Solid
How To Beat Him/her: Sorry, "Twin Snakes" Psycho Mantis, but your Playstation counterpart was much harder. (We weren't given the option to switch between first and third-person back then.) Most, if not all bosses, put up a front and claim to be un-defeatable.
But with Psycho Mantis, it almost seemed believable. Nothing worked, and where Metal Gear Solid's jewel case saved our ass on one occasion, it wasn't helping us with this one.
But, somehow, we learned. Whether through the game's strategy guide or a friend, the answer was in front of us the whole time. Just switch controller ports, and Mantis' superhuman abilities become useless.