To start working towards this achievement you’ll need to spend at least 10 skill point coins so you can unlock the assassinate ability. This ability is found in the "Power" section of her skill tree. Once it is unlocked, there will be dark spots in places of the game with floating silvery specs. If Lori stands in there you will notice she goes transparent and if an enemy is near you, press and she will assassinate the enemy. The more the ability is upgraded the more often she will manage to pull it off.
You can also unlock this achievement by standing in the dark spots and using your knife throwing attack by pressing . Each kill you earn with the knife, whilst transparent will count towards this achievement. If you haven’t unlocked this after the first playthrough you can keep replaying episode 2 as it is the quickest.
You can also just work on your Assassination kills while playing Survival mode. Select survival mode, choose the first area and Lori as your character. There are shadows in the top left and right corners of the small area and an unlimited amount of enemies to kill. If no one is close enough, just pop out of the shadows so they can see you and then walk back in to hide again. You can even heal yourself (assuming you unlocked the ability) if you run into trouble.