In order to get this achievement you have to play on Normal or Hard difficulty, so I suggest you play on Normal to make things easier. This game is a lot like classic Command & Conquer, so you can usually spam tanks because they are good against vehicles and buildings and can crush infantry. Before you unlock the Heavy Tanks, you should also include some anti-air in your composition, because tanks can't attack air units. Rocket infantry are very good but you have to be careful so they don't get squashed or mowed down by turrets.
I made a full campaign walkthrough if anyone is having trouble getting this achievement on a specific mission: