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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The Fume Knight from Dark souls II. I was only able to beat him at full hollow, completely naked and using a spear after thirty or so tries.