You'll probably unlock this achievement during the normal course of play (especially on HARD or HARDCORE difficulties), but there is a quick way to unlock it if you've finished the game at least once.
Start a new game on any difficulty, and take the passive Acrophobia Perk and the active Lucky Bastard perk. The former is so you start will less health. The latter is to ensure a one hit kill.
Start off by playing as normal until you take enough damage to be relatively low on health
Now, simply walk until you find your next enemy, then retreat. Try to find at least one food item in an empty room for safety sake. Now, walk around until you run out of hunger points, then keep walking until you damage yourself so you only have 5 hitpoints or less left (we took Acrophobia to make this process faster).
Once you hit less than 5 hitpoints, eat food so you don't kill yourself, then activate your Lucky Bastard Perk (to do this, press
to enter the inventory, click on the first "up arrow" menu to enter the character screen, then click on the shamrock icon at the bottom left). Now walk over and attack the nearest enemy. They will take 1000 damage from the Lucky Bastard perk and instantly die, unlocking this achievement.