The first opportunity to obtain this trophy is during the mission Mad Dogg's Rhymes. The game should teach you how to perform stealth kills by popping up the controls when you attempt to silently kill the first guard in Mad Dogg's mansion with a knife from behind. The trophy will unlock as soon as you successfully stab him.
However sometimes the game does not give the popup explanation and it will not pop it up after the first guard. In case that happens the controls are: L3 (push left stick in) to crouch, R1 to target the enemy and then press circle for stealth kill.
If you just knife the enemy repeatedly while he turns around and shoots you then you did not perform the stealth action correctly and the trophy will not unlock until you do so. However it is possible to earn the trophy from other enemies in the game.
Thanks to Kornfan2007 for the additional info.