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