This achievement requires you to kill "small" animals. These are basically rats, frogs, etc, which tend to blend in with the environment unless you go looking for them.
I managed to get this on the Back Alley Jazz mission in New Orleans. I got Kate's disguise and then ran around the city on full zoom looking for rats skuttling about. There are very few of them (about 12-13) that I could find, they tend to be found around crates and barrels. Make sure to keep runnning over them until they visibly splat. Achievement will pop as soon as you've splatted your 10th one.