Two of the hardest things that I have ever done:
1) Beating Omega Weapon in Final Fantasy VIII. It took me a long time before I finally figured out the best strategy and even with that strategy you needed quite a lot of pure luck to beat him.
2) Beating the Frigate level in Goldeneye 007 with all enemies on max stats (1000% health, 100% damage, 100% reaction speed, 100% accuracy). I think this is probably the hardest thing that I have ever done in a videogame. It takes a whole lot of patience, strategy and skill to get through the level unharmed and every small mistake can be fatal. It´s also very discouraging if you suddenly die cause of some unfortunate, small mistake after playing it perfect for like 45 minutes.