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