This can theoretically be earned on any level, but for the soonest and easiest method, this can be earned in "Crew Expendable". To save time, and earn three achievements at once, this can be earned alongside:
You will likely want to attempt this on Recruit difficulty. Simply run through the mission, using nothing except for the knife to kill enemies. Let your team carry the weight, and they will clear the level fairly efficiently. Just run up to stab enemies, and hide behind cover when near a group or hurt. Dying will not void the achievement, however. Just keep your finger off the trigger to avoid firing when startled, and do not use grenades or flashbangs. The trophies should pop after jumping to the helicopter at the end of the mission.
Feel free to ask any questions, and add me on TT/ TA/ PSN/ XBL as Danokitty. Happy hunting!