In 5-1, near the beginning, you'll come across a buzzard sitting on a platform overlooking a wide room. It's extremely obvious, Sam mentions the enemy by name and there's a life bar on screen.
From the entrance of this area, you will want to boost to the left immediately to a small enclosed room you should be able to see right away.
The room has a long horizontal open window with two turrets and several grunt robots in it. Toss a couple of frag grenades through the window, and immediately use the console near the door to open it. If there are any remaining robots, be sure to kill them very quickly, since speed is pretty important here.
If you grab one of the turrets and point it at the buzzard, it'll take a bit of damage before it gets up and lands, and thus invalidating the achievement.
So, before you get on the turret, toss an EMP grenade at it to stun it, then turret it for a few seconds. Before the EMP wears off, get off the turret and toss another one to restore the stun duration. Then turret it again.
Repeat until you have it killed. In my case, it took 3 EMP grenades before I had killed it. The achievement will pop immediately afterward.
*** EDIT ***
Al Soure has informed me that the buzzard moving is based on it's remaining health, not time as I originally thought. The buzzard will only move after 50% of it's health has been drained. In order to conserve EMPs, you can turret it until it's just got slightly more than half of it's health left, and then start the EMP stunning process, which should reduce the amount of EMPs you need to 1 or 2.
Thanks to Al Soure and Asuka Langley for this correction.