As stated in the achievement's description, you mustn't use any cigarettes during your playthrough. Cigarettes are used to regenerate your Stress meter (The green icon with the brain which is relative to your aiming and sprinting) but also decrease your health by a tiny percentage.
It is important to note that your character won't automatically smoke cigarettes
, whether by picking some up or having them in your inventory. However, if you don't want to accidentally smoke one while navigating your inventory (
, Consumables), then you could, as SolaceConquest suggested in his solution, discard them by pressing
or ignore the packs when searching in houses, camps, etc.