Here is the full list of all 10 Survivor Island achievements.
Cut your first tree on the island
Build your first fireplace on the island
Build your first axe on the island
Build your first shelter on the island
Build your first pickaxe on the island
Build your first torch on the island
Build your first warehouse on the island
Survive ten days in the island
Collect one hundred or more apples on the island
Bad things happen