I just played a match with my M12 - a tier 7 American artillery.
I killed all 3 enemy artillery, one of which was a tier nine, as well as a tier 7 TD.
I did not get this achievement, nor this one:
Therefore one or more of the below must be the case:
1. The achievement is buggy (wouldn't be the first time)
2. You cannot get this achievement while playing as artillery.
3. Enemy artillery kills do not count towards either achievement.
4. 2 of the tanks I killed were American. Perhaps you have to kill 4 tanks of a different nation.
Because of this I would recommend simply playing as your favourite American tank. A personal favourite of mine is the T1 Heavy. If you can get into a tier 4/5 match you should be able to get 4 kills easily....so long as people don't steal your kills.
If you don't mind waiting, and you have this/these tanks in your garage, then the T1-E6-X or X1 will also be good. The only problem with this is that every match at the moment has at least 5 X1's in it as people play with their new toy. Wait a week or so until it dies down and you should be able to get your 4 kills.
Since this is a new achievement can people please let me know how you got/get it and I will update this solution