This trophy may take you an entire play-through to unlock, but that's fine. It's a cumulative trophy so you can do it in 20 play-throughs if you so desire.
To get a stealth kill you need to crouch (by pressing
) and get close to an enemy. Once you are close enough it will say "Press
" on the screen to perform a stealth kill. Once you stealth kill your 25th enemy you will unlock this trophy.