Your first objective in "Cleaning Up the Berg" is to reach Liar's Berg. Follow Claptrap as he exits the barge through the back door. Listen to Handsome Jack announcing the million bucks Bounty on your head, and also to Captain Flynt who who wishes to claim the bounty and orders his men to hunt you down.
Some Bullymongs ambush your party. Defend Claptrap, killing any Monglets and Brat Bullymongs you encounter. Soon you arrive at Liar's Berg. There are glowing rocks around the path, be sure to smash them for loot. Continue on the road and arrive at the gate to some camp. Claptrap calls out for Hammerlock, who asks you to kill Captain Flynt's bandits. Secure Liar's Berg.
The small camp is full of Marauders. Run around the camp killing them, as well as any Bullymongs that join the fight. Then, speak to Hammerlock who asks you to come to his shack. Claptrap gets disabled after it crashes into an electric fence. Meet Sir Hammerlock. Sir Hammerlock comes of his shack and introduces himself. Apparently he came to this region to research Bullymongs and was attacked and imprisoned by Captain Flynt.
Sir Hammerlock opens the gate. Give Hammerlock Claptrap's eye (To give Hammerlock the eye, just approach him and you should see the command "Give Claptrap's Eye" pop up). Wait for repair.
After Hammerlock repairs Claptrap (by sticking in the eye back in the socket), he suggests turning the main power back on. Wait for power. After he flips the switch, power to the town comes back online. Go to where Sir Hammerlock is standing, near the bulletin board. Note that the bulletin board does not work yet. Sir Hammerlock tells you the bounty board's broken and to speak to him instead if you want any jobs.
Talk to Sir Hammelrock, and turn in the quest. You get some xp, money, and a white (common) shield as your rewards.
This completes the mission, Cleaning Up the Berg.