This achievement counts for DESTROYING modules or KILLING crew. Damaging modules or injuring crewman do not count.
Any tank is capable of earning you this achievement but accuracy is better than power. I'll explain shortly.
I rotated between 5 different tanks:
The KV-1 with Deadeye, Eagle eye and HEAT rounds.
M4A3E8 Sherman with Deadeye and HEAT rounds.
T18 with HEAT.
T82 with HEAT.
Valentine AT with HEAT.
HEAT rounds are expensive so make them count.
APCR and AP round work wonders as well but I found they only damaged half as often as HEAT rounds.
I had Eagle eye on my KV-1 and it proved invaluable. Eagle eye lets you see modules already damaged and broken. It doesn't tell you if that crew member in the spot is dead but by shooting a damaged module you have a far better chance of breaking it again. And if it was repaired after someone else broke it, you breaking it again will count towards your personal score of breaking things. But each module only counts once per tank, PER PERSON!
The strategy you want is to get up close and personal if you're certain you can survive the match up. I had far more success pumping rounds through the small module portions on the front than firing from a distance. The close distance increased my accuracy, sometimes decreasing my fire rate, but I also almost always scored a hit for two broken items. This means I was destroying the sight and the commander, the engine and the driver, the turret and the gunner, etc. Aiming at fuel systems was nice, as any fire you start can burn on and completely destroy modules before the tank is destroyed, each module again counting as one. The Xbox One has the nifty achievement tracking feature which tells you when you break a module or kill a crewman. Keep the achievement tracker snapped if you want to make sure your hits are destroying not just damaging.
If you see a tank with a damaged module at a distance (using eagle eye) and you know you haven't hit it, try to break it. I found every other shot that directly hit an already damaged part would easily break it again. No tracks don't count, but if you track a tank that is facing you and hasn't spotted you, have fun sighting in each module then re-tracking the tank to keep getting pot shots before it explodes.
Some people feel fighting front on is fool hardy and normally I would agree with you, but the goal is to break or damage modules, not kill lots of tanks. Most of the modules for many of the tanks are right in the front:
Commander's Hatch/Cupola, Gunner machine gun, Gunner port (tiny little sight next to the tank's main turret n some tanks), Tank's main turret (knock that out and your opponent can't shoot you and when it repairs their accuracy will be WAY off), Slot for the driver to see, sighting viewport, driver's mantlet, shoot between the turret and the main tank body to break turret rotation, shoot the back of the turret to destroy coms and kill the radio man, direct shots on the rear have a chance to destroy the engine or start a fire which can destroy many other modules.
If during your brawling you become disabled or begin being lit up by more enemy tanks, focus on breaking as many module as you can. This means targeting multiple tanks before finishing one off. Using a combination of everything above and while in my KV-1, I was able to get 16 in one battle.
It is still a terribly grindy achievement but hopefully this solution helps make it a tad easier.