Legitimate Method: Play slow and methodically, staying cautious on corners, peaking ledges/walls in gunfights, and keeping your sights up ready to engage.
Easy Peasy Cheesy Method: Play the level on recruit and just before triggering the mission ending, switch to veteran difficulty. Another person (ninja) had mentioned something like this before (in the now deleted post), and didn't think this would work given its large amount of downvotes. I then attempted it, and successfully unlocked it. Side note, I don't know if this may affect it but i did go into the levels starting on veteran, switch to recruit, and then switch back to veteran before level completion. It will NOT show on the mission select screen that the mission was completed on veteran, BUT rest assured they are being counted as completed on veteran for the achievements overall.
TL;DR : Play levels on recruit, switch to veteran before beating level.
Happy Hunting!