|7||948 XP, $19, Assault Rifle or Shotgun|
Start off the mission by going through the nearby travel point to get to Three Horns - Divide. Head forward a little bit and the bridge above you will get blow to pieces, so you'll need to find another way to get to Sanctuary. Fortunately, the mysterious woman from before mentions getting a vehicle from the nearby Catch-A-Ride. Follow the trail below the bridge, watching out for the Bullymongs, until you come to the vehicle spawner.
The only problem is that you can't get it to work, since you don't have access to it. However, a solution arises, as the mysterious woman mentions a nearby robot that has something that can help with her hacking the Catch-A-Ride. Unfortunately, there's another problem, as the camp the disabled robot is in is overridden by bandits, with a new type being introduced here, the Nomad .
These Nomads aren't the tougher versions that you will meet later, but they can prove to be a pain, due to their heads being slightly covered, plus the fact they move around a bit. Clear the camp of the bandits, then locate and loot the robot, returning to the station to place the device in the Catch-A-Ride. Wait for the woman to hack the machine, then access it to spawn a vehicle (the one with the rocket launcher is better).
Take some time to get used to the vehicle's controls, then jump the gap that was once the bridge. Note that killing enemies while in a vehicle will grant you less experience than on foot, so if you want the full XP, then get out and kill the enemies on foot. Drive through the canyon, mowing down the Bullymongs in the way, until you come out into a huge, open area on the other side.
For now, head to the waypoint marker and use the intercom to try and get past the gate, only to have to help rescue someone out in the area you're in right now. As you make your way to the marker, you'll notice that you have to abandon your vehicle, so do that and continue to the marker to find an ECHO recorder on the ground. This ECHO belongs to Reiss and he mentions going through the Marrowfields.
Luckily for you, this is the area right next to you, so keep going until you happen to find him. He is being attacked by three Psychos, so kill them and talk to Reiss to find out the power core has been stolen. You will receive your first optional objective for a mission here, requiring you to kill 20 Bloodshot bandits in the nearby camp, which you'll be going to anyway to retrieve the power core.
Considering the bandits aren't going to just let you waltz in and snatch the power core, you might as well just kill the 20 needed to fulfill the optional objective. You'll find a mix of Nomads, Marauders and Psychos in the camp, so you know how to deal with all of them by now. Pick up the power core and return to the gate you couldn't pass earlier, except you will be able to now. Travel to Sanctuary and talk to the guy here, who asks you place the power cell, then talk to him again to finish the mission.