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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Krauser, resident evil 4 on ps2. On the professional difficulty. I was trying to get the laser weapon. I died 69 times total between the two fights. Not only is it hard on pro, but I had barely enough ammo/herbs. Finally did it though.