Here is the full list of all 19 Mahjong Riichi Multiplayer achievements.
Get a Mangan
Get a Haneman
Get a Baiman
Get a Sanbaiman
Get a Yakuman
Win 100 Hands
Get a Kokushi Musou
Get a Suuankou
Get a Daisangen
Get a Shousuushii
Get a Daisuushii
Get a Tsuuiisou
Get a Chinroutou
Get a Ryuuiisou
Get a Chuuren Poutou
Get a Suu Kantsu
Get a Tenhou
Get a Chiihou
Get a Renhou