My advise on this: Keep tossing grenades on anything that flies during the entire campaign. I tried to kill pretty much everything airborne with grenades (died a few times in between) and got lucky at the start of Chapter 3-3.
I'd speculate that either the achievement description is wrong and you have to kill more than 10 flying targets or the game measures the distance between you and the enemy (e.g. if you are hovering and destroy something below your position it might not count). But those are just speculations, after all the achievement seems to be pretty random ô_o
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