A really quick and easy way to get this that I found is in the Red Zone. At coordinates 537, 416, there is a tank that has an infinite spawn there. Go there, jack the tank (stealth of course), and then move onto the street that is directly to the east of that tank. If you ride north on that street until his spot is off your map, then drive back south to his spot, the tank will have respawned in the EXACT same position! And what's better is that you can kill him with no worries of ever becoming hostile. If you want to play it safe with his spawn, drive north until you get blocked by the giant... tentacle thing that's grabbing the building, then drive back south. I got the 10 kills in about 8 minutes! Happy hunting!
As stated by TheMajinLegend below: "in my case I was able to kill a tank once at each end- for example one tank at the location listed above and then another tank at the mutant bean stalk". So try your luck with that, and you'll get it even faster!
ALSO stated by Whistling Wolf: " when you reach the "bean stalk" and shoot the tank there, on the way back a chopper heads your way that you can shoot down as well." Just another way to make this achievement really fast.