Exit the studio and head toward the Founder's Island (you cannot rely on the Batmobile now, so use gliding and the Grappling Hook). On your way to that destination watch out for stationary turrets and flying machines patrolling the area.
When you get close to the designated area, land on a rooftop and check the current location of the relay drone. Glide toward it and try landing on it. This is not so difficult, as it is flying slowly. Batman will automatically hack into the drone's board system and get the relay chip. This way your Remote Hacking Device will get a new function - Drone Hacker.