Here is the full list of all 40 Radiation Island achievements.
Build and place a furnace
Kill a zombie
Craft and place a storage case
Craft arrows
Upgrade your backpack
Equip a radiation suit
Use the pickaxe to mine rocks
Craft a piece of clothing
Craft the pickaxe
Hunt an animal for meat
Use the stoneaxe to cut down trees
Craft your first weapon
Scavenge resources scattered on the ground
Find food
Craft and place a camp fire for the night
Craft a torch
Cook meat inside the furnace
Use the furnace to melt iron ore into metal
Craft a machete
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
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