Here is the full list of all 20 Legendary Mahjong achievements.
Match the first 2 tiles.
Restore the Temple of Earth.
Restore the Temple of Time.
Restore the Temple of Water.
Restore the Temple of Fire.
Restore the Temple of Wisdom.
Restore the Temple of Air.
Restore all the temples.
Unlock the Celestial Gate.
Complete all levels in all the temples.
Get a new rank.
Get the highest rank.
Match 10 Ice Tiles.
Match 10 Lock Tiles.
Use 10 Magnet Tiles.
Use 10 Whirlwind Tiles.
Open 10 Box Tiles.
Restart 5 times.
Undo 100 moves.
Match 10000 tiles.