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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Tales of Vesperia, final boss Duke Secret 3rd form (have to collect all the Devil/Fell weapons through out the game) Literally harder then you would ever believe, it's a live action JRPG (Japanese roll playing game) if you don't know, the story and character development are amazing and the combat is like a fighting game, very cool. Anyway this guy hits you and he hits hard I might add, and inflicts every single status effect in the game on you or any character he so much as looks at haha