I still remember fighting Psycho Mantis in Metal Gear Solid 1. He would read all your moves before you did them and was literally impossible to beat. He would also talk to you about the games that you had already played by reading your memory card (this was super trippy). The only way to beat him was to unplug your controller and plug it into port two so he couldn't read you moves anymore. It took me and my buddy days to figure it out... This was before Google too, so you couldn't just look it up.
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Ever play Runescape? By far one the hardest bosses I have ever fought was the Kalphite King on a day the games severs were being DDOS'd and me and my mates were trying our hardest not to die and if one of us did we had to hold off on our own til they made it back I think we actually managed to get that kill.... Good times