Command & Conquer: Red Alert 3

Easy and fast solo method:

1v1 versus Medium Warren (Allies) on Industrial Strength with 10k starting resources. I used the Rising Sun since they can build so fast with nanocores, but you could use Allies or Soviets just as well.

Start with a normal buildup. Generator > Barracks > Refinery, and so on. Build 10-15 infantry of various class to defend the front of the base while you continue building. The goal is to build 8-10 Guardian/Hammer/Tsunami tanks. You can queue as many as you want, but I didn't need more than this. You can build whatever else you want at this point (backup tanks, defenses, engineers, etc.)

Warren will initially build a lot of Attack Dogs and other infantry to scout the map, followed by Riptides to attack any refineries and captured buildings you have outside your primary base area. That's OK, you can ignore them all unless they attack your core base.

Once you get the tanks built, set them all to Hold Fire stance and roll out. Run down as many infantry as you can by telling your cloud of tanks to move behind the infantry. You can stop to destroy any occupied buildings as well. While you are doing this, make your way towards Warren's base.

By this point, he will probably have built an airfield with some Vindicators. As you roll into the base, squish as many infantry near the front entrance (AI always seems to put a Barracks there) as you can, and then go directly to the airfields. Destroy them and then the MCV/Armor Facility so he can't rebuild anything. The Riptides will return to defend their base (to no avail.)

Most likely you will have the achievement by now, but if you haven't, each destroyed enemy building will leave an infantry to squish. If you get down to only one building (most likely the refinery on corner of island) you can roam the map looking for stray infantry.

Starting with 40k is a bad idea since the AI can build crazy fast. I tried this once and was met with an army of Cryocopters. If you don't build and attack fast enough, you may encounter Cryocopters anyway. Don't forget, you can also squish infantry with Ore Collectors, Nanocores, and even your MCV if you don't have any tanks in the immediate area.

Good luck. It should take around 10 minutes.

I personally followed Mr Midnight 1's guide as shown in the thread.
The only acception is that when playing as the allies', the chronosphere's kills on infantry by teleportation count towards the crushes, do this on a large enough group of men each time and you should easily unlock the achievment.

Any questions message me on Xbox Live on the gamertag system52

The best way to do this is to set up a skirmish match with you playing as the Soviets and the CPU playing as Allies, medium difficulty. Build enough of a base to obtain Hammer tanks, and train plenty of them.

As the enemy AI sends infantry and light vehicles to attack you, simply move your Hammer tanks through them (target behind the enemies). Setting hold fire stance should help you minimise kills by cannon.