I just wanted to post this up for people that want to do the achievement on their own. You can set up a local splitscreen match if you use a second controller and profile. Have the extra profile start up as a level 1 character and have your level 50 character that you normally use join that game via splitscreen. Run through the opening to the game takes about 2 minutes (with your level 50). The first travel point "inside" Fyrestone near the doc's place will allow you both to travel to the Underdome. Once there use your level 50 to role over the opposition. I timed each round takes 8 minutes to complete on average so your looking at 40 minutes each for the small challenges and 160 minutes per large challenge. I did this with a Berserker so your results may vary based on your character. There are great choke points available because some of the waves later can be overwhelming.
Gully: rocks on lower level far left of the stage can be hidden behind by jumping through rocks or jumping off cliff to get there. Great for level 15-20 horde waves.
Hell-burbia: far left of the stage use the crates at the top of the stairs to jump on top of the building (thanks indigoX00)... avoids enemies spawning next to you and avoids horde waves.
Ruins: to the far right of the stage in the middle of the board use the ramps. If facing the ramps use the left ramp, here you can jump up onto the ledge just above the platform to avoid horde waves. Also the bottom of this ramp obscures enemy line of sight and is a good place to regen shields if you get caught off guard.
Final tips: Take in class mods that regenerate health depending on your class or just use your berserk (for you Berserkers out there), this helps deal with the ever annoying double modifier given out by Moxxi of vampire (constant life loss but killing an enemy regens health) and no shields... this can be deadly to a single player, if the enemies spawn far away from each other.
Lastly since you are the only player you can pause the game and take breaks doing it this way
IMPORTANT NOTE: I have tested and confirmed a level 1 character can travel to the Underdome. Here is how: Step one sign in a secondary profile as controller 1 and start up a splitscreen match. Then have controller 2 join as a level 50 (or whatever level that has fast travel ability). Start the beginning of the game... use the level 50 only and go into Fyrestone passed the opening sequence. Use the fast travel post in front of the doc's place once your INSIDE Fyrestone. Only the level 50 can start the fast travel process, but once you do, it takes both the level 50 and level 1 to the Underdome. The enemies will still be roughly level 12-15 starting out. Hope this helps clarify have a great day everyone.