Here is the full list of all 40 Radiation Island achievements.
Use the pickaxe to mine rocks
Craft a machete
Craft a piece of clothing
Upgrade your backpack
Hunt an animal for meat
Equip a radiation suit
Craft arrows
Craft the pickaxe
Use the stoneaxe to cut down trees
Craft your first weapon
Find food
Scavenge resources scattered on the ground
Craft and place a storage case
Craft and place a camp fire for the night
Craft a torch
Build and place a furnace
Cook meat inside the furnace
Use the furnace to melt iron ore into metal
Craft a shovel
Dig for sand on the shores
Harvest resources from the plants on the island
Craft bandages from leaves
Craft medicine
Craft string from fiber
Craft a fishing rod
Craft a bow
Catch a fish with your rod
Melt sand in furnace to obtain glass
Craft a stone spear
Kill a zombie
Reach the center
Craft and place a sleeping bed
Find a machinegun
Find a revolver
Craft the spyglass
Craft the tesla weapon
Convert crystals to other materials
Disable one tesla tower
Visit another island
Activate the central teleportation machine