APC stands for Armored Personnel Carrier. They're the armored, tank-like vehicles with wheels that usually show up before the tanks do. They're pretty common whenever Blackwatch has any sort of vehicles around, though they're probably more common in the Yellow Zone than the Red Zone.
There's a really easy spot in the RZ...I wish I could tell you specifically where it is, but it's near a base (on top of a building). There's an unmanned APC, and a helicopter down the road. You can drive back and forth between the two and they keep spawning, but killing them doesn't raise your alert to Red right away. --- But Mommy, I don't want to go to school today. I want to stay home and bake cookies with you.
You can get a good headstart towards the goal of 10 vehicles by Stealth Hijacking (military disguise) a Tank or APC in a base that has some of target vehicles (Tanks, APCs, helicopters) parked in the lot.
Hijack a Tank or APC and start shooting the parked vehicles first.
The trophy does not say that these 10 vehicles have to be attacking you!