This will be your first achievement in the DLC, first you will need to travel to 'The Underdome', once there head to the bounty board to start these off.
Now the enemies in the tournaments scale with the host of the game so if you want this to be easier play in xbox live/splitscreen co-op and have the host be a low level, like 10.
For this achievement you need to complete the smaller tournaments for all 3 maps (Hell-Burbia, The Angelic Ruins, and The Gully) the smaller tournaments are only 5 rounds each with 5 waves of enemies:
◾Wave 1 - Starter wave - Simple foes to start off the round
◾Wave 2 - Gun wave - Enemies have guns
◾Wave 3 - Horde wave - Sends many psychos
◾Wave 4 - Badass wave - Many badasses and high-grade enemies
◾Wave 5 - Boss wave - Summons a boss from the story onto the stage.
You need to complete each area in one sitting so be prepared to spend around an hour on this.
All of the tournaments need to be completed with the same character BUT you do not have to do all the rounds as you can join someone who is on the last round of each arena so long as they havnt finished the last wave, ie you can join round 5, wave 5 and complete each arena.