You gotta fly through tight spaces between buildings, or pull off the "cut the engines" in 3rd person view and hope you can evade it and mash the accelerate button and hope you gain altitude before you smash into the ground.
When I was watching the live feed today, there was this mall that had a mostly glass facing, the dude flew the chopper low to the ground through the entrance, elevated inside and starting tearing everyone up. XD . The DICE commentators went crazy with amusement. He eventually crashed into a wall because he was trying to shoot out the glass ceiling, and looking up of course is reverse.