After completing the Assault the Authority Bridge, pick up the Authority Pulse Rifle and talk to Captain Marshall to start this job. Make sure you've loaded up on ammo and head out to the Wasteland and Capital Prime.
Once you get into Capital Prime, it's pretty straight forward. Kill dudes and move along, when you come to lasers blocking your way, there's a switch nearby. No final boss, so you can be pretty liberal with ammo use.