These little things look like spiders or facehuggers from the Alien films and can found throughout the campaign and mulltiplayer. Simply kill 31.
For easy kills, simply start up mission four (Gone Rogue). Advance to the part where you enter the Umbrella Facility. The room with the T-103 Tyrant. Extract with the parasite from the Tyrant with the large Syringe, don't go to the next objective marker. Instead round around in circles and kill either the Parasites or Parasite Zombies, they will spawn indefinitely. Do so till your desired achievement pops.
Note: Eventually you will run out of ammo, then go to the next objective, trigger the Tyrant and go for the keycards, kill a few parasites, and go to one of the red-lasers to kill yourself. The parasites will only respawn after you triggered the Tyrant. Rinse and repeat!