Act 1 - "The Bog":
A short time into the level, you will reach an area full of cars and a freeway overpass above and behind it. After clearing some enemies, Cpt. Price will call out that one of your teammates is down. Go to the front of where all the cars are to find the Stinger missile launcher. Quickly head to the building on your left, then your first right, then on your immediate left there will be a stairway to the second floor. Aim at the first tank you see, keep it centered until it locks on, and release. Repeat this quickly for all 4 tanks. If one drives out of your line of sight, just restart the checkpoint, and try taking them down in a more efficient order.
The trophy should pop as soon as the last tank explodes.
Feel free to ask any questions, and add me on TT/ TA/ PSN/ XBL as Danokitty. Happy hunting!