Are you guys sure you should be talking about the S. Q.? (You know, from PM2.) Maybe you should at least put spoiler warnings.
Some hard challenges I have completed:
SSBM: Beating the last two event matches. Beating Classic Mode on Very Hard. Beating All-Star Mode on Very Hard. Beating teams of 3 Level-9 CPUs in VS. Mode (I once got a score of +5 as C. Falcon, I believe). Defeating my neighbor/friend in VS. (he's GOOD).
SM64: Getting all 120 Stars. Getting all of the red coins in the Wing Cap Switch Course (and pressing the switch) on the first try.
SM64DS: Getting all 150 Stars.
MK:DD!!: Unlocking everything in the game.
MvDK: Clearing all the stages and getting everything (no outside help).
Some hard challenges I haven't completed:
SSBM: Beating Adventure Mode on Very Hard (haven't tried yet). Beating
Normal Classic Mode without dying (that horrible Crazy Hand!!!). Getting all the trophies.
SMS: Getting all the Shines (it will be so HARD to get 100 coins in Gelato Beach, find all the blue coins, etc.!).
That's all I can think of for now.
Ever notice how the name "Playstation" sounds more kiddy than "Gamecube" or "Nintendo 64"?