To get this achievement, you have to search a dead elite, by standing over him and holding A. The bit that makes this tricky is his body evaporates pretty quickly, so you don't have much time to get to him after you kill him.
I got this on Level 2, Church of resurrection. Before the first safe house you will progress down and alley and then it opens into a road, with the marker behind a door at the end of the steet opposite. First, and key is to clear out all the normal undead, then approach the door - this means you can just worry about the elite. The elite Nazi (with the MG42 machine gun) will appear and you should run back to the sandbag platform behind. Crouch using B and using your sniper rifle try and headshot as much as possible, ducking back if you are getting hit. He never advanced to me, so you can play cat and mouse until he goes down, but as soon as you see this run to him (push thumbstick down). Good luck!