This requires the use of the game's multiplayer function with 2 DS's. Start a Classic game and turn on Challenging. Let the profile you wish to level up do moves, playing all seven of his tiles each turn for massive numbers of points. When it comes to the other player's turn, simply have them pass. Repeat this cycle as needed to greatly improve your game stats, including your level, allowing you to better unlock avatars and themes.
During gameplay, raise your level by winning games to unlock these character avatars.