Here is the full list of all 9 Mahjong Club achievements.
Check instructions of all yaku in the tutorial.
Complete the shuffle practice once in the tutorial.
Change the table pattern
Achieve a yakuman.
Achieve a 'last self-draw' or 'last discard'.
Achieve a 'dead wall draw'.
Finish the game in East Round 1 and win the first place.
Reach North Round 1 of the game.
Achieve a 'hand of heaven'.