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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Rocket Racer from some Lego Racers game in the 1990's. The way they programmed that specific AI was simple: "you will not win." He was that boss that needed the older Brother to beat. 4 year old me had serious trouble with him, but for some reason, after he's beaten, he gets a lot easier in rematches.