Here is the full list of all 54 MOAI 2: Path to Another World achievements.
For scoring 400,000 points
For cutting 100 trees
For opening 50 chests
For completing every Eye-Unai level
For fishing 150 times
For completing every Eye-Unai level with a gold medal
For scoring 200,000 points
For removing 50 stone blockages
For fishing 50 times
For scoring 100,000 points
For scoring 60,000 points
For scoring 30,000 points
For starting a game
For scoring 600,000 points
For scoring 800,000 points
For scoring 1 million points
For scoring 1,250,000 points
For completing every level Beach-Nui level
For completing every Subte-Rain level
For completing every Miru Kingdom level
For completing every level
For building 300 buildings
For gathering more than 10,000 units of food while playing a level
For gathering more than 5,000 units of stone while playing a level
For gathering more than 3,000 units of essential oil while playing a level
For gathering more than 5,000 units of mana while playing a level
For gathering more than 5,000 units of wood while playing a level
For preparing 100 fields
For repairing 100 quarries
For planting 100 groves
For making 100 trades at the market
For building 20 temples
For recruiting 400 workers
For killing 250 ghosts
For killing 500 ghosts
For killing 750 ghosts
For cutting 200 trees
For cutting 400 trees
For removing 200 stone blockages
For removing 500 stone blockages
For fishing 350 times
For repairing 50 bridges
For repairing 100 buildings
For playing for one hour straight
For using no bonuses during the entire game
For not clicking on the screen for 30 seconds after a level starts
For completing one level twice and improving your results
For completing every alternate level
For completing every Beach-Nui level with a gold medal
For completing every Subte-Rain level with a gold medal
For completing every Miru Kingdom level with a gold medal
For completing every level with a gold medal
For acquiring every artifact
For earning every achievement