The road to recruiting Braddock starts outside the Lucky Seven Casino. Take any agent there to kick things off.
You'll get a mission to take out a patrol. The scenario is that they're about to shoot civilians, but this doesn't seem to be an actual threat.
Mostly helltroopers, they're in an open space, and mid to long range fire will quickly cut them down to size. After some chatter, you'll get another patrol killing- this one outside what looks like a hotel. Note that three of the patrollers come with targets above their heads. Prioritize these guys- random grunts will keep materializing to harrass you until the targets are down.
The last part of the mission involves taking out an enemy vehicle. It is technically possible to do this with your regular weapons, but much easier with your own vehicle.
No fancy tactics required here, just knock it into a wall or off a ledge for mission completion.