Here is the full list of all 28 The Islander achievements.
Catch a total of 100 Fish
Catch a total of 100 Starfish
Catch a total of 100 Parrots
Buy a total of 250 Animals
Plant a total of 250 Trees
Cut down a total of 250 Trees
Break a total of 250 Rocks
Reach Level 20 in a Single Run
Buy a total of 100 Animals
Plant a total of 250 Bushes
Build a total of 750 Decorations
Plant a total of 100 Trees
Plant a total of 250 Crops
Reach Level 10 in a Single Run
Plant a total of 100 Bushes
Build a total of 250 Decorations
Buy a total of 25 Animals
Plant a total of 25 Trees
Buy a total of 200 Cocobots
Plant a total of 100 Crops
Buy a total of 100 Land Expansions
Have at least 1M Gold
Have at least 100K Gold
Build a total of 100 Decorations
Plant a total of 25 Bushes
Reach Level 5 in a Single Run
Plant a total of 25 Crops
Have at least 1000 Gold