You'll start finding Vodka in desks within the Exhibition complex. Finding two during the missions "Hands Off! & A Glass Darkly". Vodka can only be accessed/used from within your inventory. It doesn't seem to appear as a use item on your item wheel.
Open your inventory from the menu (
) and press (
) on the Vodka will drink it. You only need to drink one bottle to get "Drunk." The drunken state lasts anywhere between 1-2 minutes giving you plenty of time to kill 5 enemies. I managed to kill 5 of the white Vova engineers before it ran out.
The easiest location is during your second encounter with Sprouts, in the Exhibition halls. Just drink the Vodka before walking into the "Mother" filled rooms. Shoot a few Sprouts/Mutants and the achievement should pop.
Vodka Locations:2x Exhibition Complex Entrance (Desks)
1x Pavlov Medical Wings (Desk)
Testing Ground Lootyagins