First off, the obvious solution of playing as Claptrap does not work. While he doesn't need oxygen, he also doesn't suffocate.
The easiest method is to use 10 moonstone to purchase the Squil Syrup cocktail from Moxxi's. It heals you for 0.8% health per second for 30 mins. This is faster than the lack of oxygen will damage you. Just sit around and wait for the achievement to complete.
If you don't have 10 moonstone, it's very easy to farm it in the Triton Flats area nearby Concordia. Periodic meteors will fall, and upon breaking will drop gold chunks and often moonstone.
The alternate, harder methods are having enough HP to just last 5 minutes, or use various healing perks. Not recommended though.