To earn this trophy you need to get into a chase with an APC. Whilst on the chase they will call backup, its the backup vehicles that you need to smash into the walls to earn the trophy, not the main armoured troop carrier.
You need to use your batmobile to destroy them, and not your homing rockets.When the vehicles pull along side you, just press the coresponding buttons to smash them out of your way. Once you've destroyed 10 militia transport vehicles the trophy shall be yours
Below is a video I found on youtube fro AFGuidesHD that can explain and show you how to get it.