Here is the full list of all 71 MOAI V: Collectors Edition achievements.
For removing 500 stone obstacles
For healing 100 workers
For crafting 30 artifacts
For making 50 trades
For using the Nature Elements Temple 50 times
For repairing 75 gold mines
For building 300 buildings
For building 75 forges
For building 75 sawmills
For preparing 75 fields
For scaring Kra-Ken
For completing one level twice AND improving your results
For repairing 75 quarries
For using the windmill more than 25 times while playing a level
For making 50 sacrifices
For chopping down 400 trees
For building 10 temples
For picking the fruit off 75 trees
For repairing 30 bridges
For completing every level
For completing every level with a gold medal
For completing every bonus level
For recruiting 300 workers
For completing every level of the fourth chapter for Hika-Ri
For completing every level for Hika-Ri
For planting a giant bean
For making every artifact
For gathering more than 10,000 units of food while playing a level
For hiring more than 20 workers while playing a level
For completing every level of the third chapter for Hika-Ri
For putting out 30 buildings
For producing more than 6,000 units of ore while playing a level
For collecting more than 5,000 gold coins while playing a level
For completing every level of the fourth chapter for Kao-Ri
For completing every level for Kao-Ri
For collecting 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 collecting more than 5,000 units of stone while playing a level
For using 10 magic signs while playing a level
For acquiring every magic rune
For forging 10,000 units of ore
For learning every magic sign
For completing every level of the third chapter for Kao-Ri
For removing 200 stone obstacles
For taming 100 of Manu-Ai's magic animals
For making 100 exchanges with the collector
For completing every level of the second chapter for Kao-Ri
For fishing 150 times
For opening 200 chests
For building 10 lighthouses
For playing for one hour straight
For chopping down 200 trees
For fishing 100 times
For completing every level of the first chapter for Kao-Ri
For repairing 100 buildings
For completing every level of the second chapter for Hika-Ri
For feeding Kra-Ken
For crafting 10 artifacts
For producing 6000 gold coins
For forging 5,000 units of ore
For producing 3000 gold coins
For forging 1,500 units of ore
For fishing 50 times
For completing every level of the first chapter for Hika-Ri
For producing 1,500 gold coins
For chopping down 100 trees
For removing 50 stone obstacles
For building the Fire Gate
For clicking 10 times on the same active object
For not clicking on the screen for 30 seconds after a level starts
For starting a game