Here is the full list of all 32 Len's Island achievements.
Collect 20 Glass Bottles.
Kill 100 Enemies.
Do 100 rolls.
Collect some wood.
Kill 500 enemies.
Collect 1 Lightstone.
Collect 50 Lightstone.
Defeat the Voidboar.
Get a Blackjack.
Lose 500 Coins on Blackjack.
Get 10 Blackjacks.
Die to Bees.
Eat 50 Blue Berries.
Plant 1,000 Crops.
Get Killed by a Tree.
Buy the Voidpack.