This is a fairly easy achievement to get, as I got it within 30 hours of the game's release, granted I played practically non-stop. But anyways I've found the best ways to level up are through simply completing main story quests, and (if you found them) the Slaughter Domes, make sure you have co-op buddies as well because that will increase your XP gain.
If you haven't found the Hyperion Slaughter Dome it is located in the South Side of Eridium Blight, just up a rocky hill. You can get to Eridium Blight through the Northwest corner of The Dust.
Take note that in the Eridium Blight, you may also come across Donkey Mong, who will award you the Definitely An Italian Plumber achievement, and possibly a rare weapon or two, he is where I found my first Orange Rarity weapon.
(Edit) I noticed that I didn't have the "Definitely An Italian Plumber" achievement yesterday, so I went back to Eridium Blight and discovered that you actually come across King Mong, NOT Donkey Mong, however he still has a tendency to drop good loot, so I recommend killing him for that reason alone.
(Edit #2) After fooling around for a while I discovered that Donkey Mong IS in Eridium Blight, and not too far from the location you generally find King Mong, take a right just before you enter the Hyperion Slaughter Dome. Donkey Mong is actually quite small compared to King Mong, but you can identify him by the barrels he will continuously throw at you.
Also, suggested by Hirsute Dave "If you stick to within a level or two of the recommended level for each quest you should be able to get a good chunk of XP for each kill without getting too overwhelmed."