You will encounter around 20 tanks in the campaign
so no need to grind this one. The best way to kill a tank is to one-shot it with a rocket or use an air strike. Just don't let the gun point at you, if the tank fires you are pretty much guaranteed to be at a game over screen.
liner bronson includes this pro tip for those having trouble:
Just to mention that this achievement glitched on me first time around. If this happens to anyone else, best thing to do is wait until you've got all the other achievements, uninstall then reinstall the game and play until mission 6 when the first tank appears.
You don't have to finish the level for the tank kill to count, just get a rocket drop, destroy the tank, then blow yourself up with one of the remaining rockets. Rinse and repeat.