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