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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Do MMO bosses count? If so, Absolute Virtue in FFXI. That thing remained undefeated for several years since no one could ever figure out the secrets required to weaken him. Also, after I had quit they shortly after released another ridiculous boss named Pandemonium Warden. I believe a Linkshell (basically a guild) went against it for 48 hours straight rotating players in and out and they ended up giving up.