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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I actually have to say some of the lost planet 3 bosses, they involved learning how to dodge the bosses attacks, sometimes fighting off other Akrids at the same time, spotting their weak point, and being able to exploit that weak point. It got tough. Like the king crab boss, you had to use your rig (a utility mech) to to grab its claws and lift it into the air. Get out of the rig, and shoot its stomachs up, it would then knock your rig over and you had to evade its attacks until you could climb back into your rig, easier said than done.