Firstly, so you are away what a spinner is/looks like, they aren't actual enemies that attack you, but you do see them around a lot and they are killable, this is what they look like.
The way I had achieved this due to missing it as I played through the campaign is I loaded up Chapter "Orick, California" then part 2 "Redwoods", (if you've not done the campaign yet, then don't worry i'll describe the area) As you progress further through the woods, you will eventually come up to a little logging/building area with a few yellow trucks, one of them having logs on the back, the other one having a Spire behind it. There's also be music playing in this area, and if you run a little bit ahead up to the bridge area (don't jump down), you'll get dialogue of the AI talking about spinners.
If you look at the ground as you go through this area, you'll see the little spinners (See picture above), just shoot at and kill as many as you can, I got about 7 kills each time, once done and you can't find anymore, run over to the yellow truck on the bridge like thing, but don't jump down, just shoot forward to attract attention, and the little flying bots should soon come over and (eventually) kill you, which keeps the kills you had just got, now you're back at the beginning of this little area and can get your kills again. Just rinse and repeat until you get the trophy.