This mode allows you to place Miis in different sizes without minigames, to compete for fast times.
To unlock a higher difficulty level for CPU players, you must beat a CPU player on their highest available difficulty in a Party Mode (Board Game Island, Globe Trot, etc.).
To unlock additional minigames for Challenge Mode, you simply have to play their normal version in any mode.
To unlock Spot the Sneak in Minigames mode, you must play ALL of the 4-player minigames. Playing them in Free-Play DOES count. Spot the Sneak is a mode for 2 to 4 players in which one player is given an advantage in the minigame and the others have to figure out who the sneak in each game was.