It's recommended making a custom loadout with prometheus vision for this achievement.
After completing the first mini objective (activating the switch) you start going back to where you came from and a Knight will spawn around the corner. You will be informed by a voiceover. At this point, crouch around the corner and use prometheus vision to watch the Knight walk back and forth, as he turns his back towards you, run up to him, and hold to preform an assassination, unlocking the achievement.
I danced around a knight in a cloak for quite some time before I #facepalmed when I realized the EASIEST way to get the Knight in White Assassination achievement: Plasma Pistol overcharge. When struck with a Plasma Pistol overcharge knights stop what they are doing and start screaming. When shot from melee range, this gives the player Ample opportunity to simply stroll around behind them and, well, "off with their head!"
Did it on Sacred Legendary got award and achievement. Use active camouflage around the end of the level there are a ton of knights. Don't let them see you first or they'll shoot you whether camo is on or not.
*Update to #16 ... Should have just watched the video. You need to make sure you do the assasination with the animation involved. You can't just run up and melee them in the back, you have to HOLD RB... not just press it.