MOST WANTED: Armored And Dangerous
Armored personnel carriers begin patrolling the streets after you finish Mission 08 - Miagani Island Base. These trundling metal husks have a surprising turn of speed when roused and can often leave the Batmobile in the dust if the driver lacks sufficient skill. The APC will roam around the roads until you intiate an attack with the Batmobile (be it by slamming into it or targeting it with a disabling shot).
When the chase is underway, you will need to stick close enough behind the APC for a slow lock on to complete before you can fire a shot, damaging the APC's health bar. Of course the APC isn't going to make things easy for you. It will call in for backup units to slow you down and deal damage. These armoured cars can be targeted the same way as the APC or simply shunted aside if you get close enough.
The APC (and cars) will also fire rocket launchers towards you, shown with projectile lines similar to those you see when engaging drones. After a second or two, they will fire. Swerve to the side or use your side thrust to move out of the way while you keep the pressure on the APC. When all of the APC's support vehicles are gone, the goon driving the thing must hit the NOS as it will rocket away, forcing you to stay flat out to keep up.
Stick right on it's tail and keep firing those immobilizers until the health bar empties and the APC goes down. Keep in mind that the number of support vehicles and rocket launcher shots will increase as you destroy more APCs. APCs take time to spawn after taking one down, so pick them off when you see them driving by while you are doing other things. They are fairly easy to take down as long as your driving skills are up to snuff.