On this page of the game guide to Borderlands 2 you will find the walkthrough description of the main mission titled Best Minion Ever - part 2. This is one of the tasks that you will complete while progressing through the Southern Shelf area.
Head up the camp while eliminating the enemies you come across. Eventually you will find a Claptrap  in the northern part of the camp. Get rid of the bullies and approach it.
Following the Claptrap, you will reach a staircase from the above screenshot. The Claptrap will order you to find a lever of the elevator on which it will be waiting. Go up the stairs and turn left.
You will reach the above location, where you will be once again attacked by Bandits. After clearing the area, go up as the arrow suggests.
Here you're in for another fight. Go up the stairs and you will reach the lever you're looking for. Use it and the Claptrap will join you.
Head up the camp along the Claptrap to reach an entrance to an arena, on which you will have to fight Captain Flynt . Behind the descent there's a vending machine from which you can buy ammo in case you need some.
Bandits will also join the fight. Be sure not to stand on the grate seen above, as from time to time fire will burst from between them. At the beginning of the fight, Flynt will be on a balcony at the very end of the arena. Shoot him a bit and he'll come down to you. After he reaches your level, use the buildings at the edges of the arena as covers to regenerate your shield.
After defeating Flynt, head to the north-east side of the arena where the Claptrap will open the gate for you. Inside you will find a weapon chest, among others.
Follow the robot further to its ship. Head onboard finish the mission by speaking to the Claptrap. Afterwards use the portal leading to Three Horns Divide