For this trophy you have to successfully use the Syringe on someone then the trophy will pop immediately afterwards.
On every level you are equipped with a Syringe and it can be found in your innovatory. Depending what difficulty you are playing the game on, the amount of doses can vary. To use the Syringe equip it by pressing to enter your innovatory, scroll until you find the Syringe and press to equip it. Be aware that if anyone sees you with it, they will be alarmed. Find a victim with his back turned from you and sneak behind him by holding . Once you are right behind him, press to use your Syringe which will put your victim to sleep.
You can run and attack with the Syringe but it is 50/50 whether it will work or not. Also if someone spots you, then your chances are blown as it becomes impossible to attack someone with it when they are running around like a headless chicken. Very much like Poisonous it would be impressive if you played the game without using the Syringe. There are many opportunities in pretty much every level where the use of the syringe would be beneficial.