Head outside the Buzzard Factory. There you'll encounter the first group of Loaders. Mostly just expect GUN Loaders for now. Things will get harder a bit farther in but this makes for a good warm up. Defeat them then turn to the East and head over Broken Face Bridge. You need to pace yourself some to Brick. He will want to run up to every enemy he can and punch them in the face: hard and repeatedly.
Cut around them or just jump over them quickly. As you get to the bend in the area you will find your first of three Mortar Beacons. Head over to it and wait for Brick to smash through the shield. When the Beacon is destroyed, another wave of GUN Loaders will come crashing down.
Follow Brick the South toward Slab Town keep on guard for more Target Circles. It's only a short run across the bridge to the second Mortar Beacon. Head over to it and destroy the beacon once Brick cracks the shield around it.
After the Mortar Beacon is destroyed then the next wave of GUN Loaders will come crashing down. Follow Brick to deal with them. You will want to keep with Brick now as another type of Loader gets thrown at you: ION Loader. These shield themselves other Loaders and shock you if you close in them while their shield is up.
Head to the South from Slab Town. As soon as you get down near the entrance turn to the West. Go over to the Beacon and wait for Brick to smash through the barrier. Follow him over to the East after that. You will have a Badass Loader to deal with. use the various containers spread around as cover to protect yourself as needed. If you have shock and corrosive weaponry it won't be too hard of a fight. Once the Loader is destroyed, follow Brick back to the entrance of Thousand Cuts. He will tell you that he'll meet you back in Sanctuary. Go over to the Fast Travel Station and use it to get back there.