You can either do this in online co-op or in split screen with a second controller.
Once in game head to
Arid Badlands if you're not already there, you will spawn at Dr. Neds place, not far from here is a bandit camp you fought at early on in the game, there will be an area to the right with a large 'ARENA' sign, it is here if you need a map
The area looks like this
Transport to the arena and once there follow the arrow around to the board and press
to setup a match and press 'Ready!' at the bottom to begin.
You'll be teleported to the arena to fight each other, there will be 3 rounds so who ever is going for the achievement needs to kill the other to win. You usually spawn at the opposite side of each other.