Here is the full list of all 11 The Island Story achievements.
Need to have 10 plants
Need to have 25 plants
Need to have 30 plants
Need to have 35 plants
Need to have 40 plants
Need to have 50 plants
Fruit production more than 3000
Fruit production more than 10000
Explore 100 times
Island trees reaches 500
Island trees reaches 800