Early on, Pikasprey figured out how to use one basic move (Struggle) to deal a lot of damage, but then there was a glitch where Ditto permanently forgot how to do that, as if the game had become self-aware and decided to f**k with him. He eventually managed to get to the end through a combination of blind luck, grinding, and having nothing better to do that week.
What about playing the whole game as Rattata, a lil rat Pokemon? Not hard enough? How about swearing that losing even one battle means it's game over? That's especially rough, because even if you spend hours leveling up a Rattata, it can still be killed by a random critical hit (the "You can't polish a turd" law of physics). It took Twitch streamer Pokemon Challenges a month and a half of many, many dead rats to accomplish this pointless feat in Pokemon FireRed. Click here for a very happy, slightly traumatized nerd. Or better yet, watch this montage of all his deaths:
Then there's the holy grail of self-imposed Pokemon torture: finishing a game using only a Magikarp, the equivalent of winning World War II with a water pistol. Magikarp sucks so hard that it isn't even noticed by certain types of Pokemon. The strategy employed by YouTuber Meikachuchu essentially consisted of pumping this worthless mess full of items until it became ... still a total mess, but somehow a winning one? That's ... almost inspiring.