This is how I earned this achievement:
(If you wait until AFTER the main game to achievement hunt, like I do, this will work for you no problem, since you will have a decent amount of health)
-Go to Moxxi's bar in Concordia.
-Purchase the Squil Syrup cocktail at the bar for 10 Moonstones (on the left side of the bar all the way to the right). This cocktail regenerates 0.8% of your health every second and lasts 30 minutes.
-Go to Triton Flats (or anywhere else that's outside), and waste all you oxygen by simply double/boost jumping. Once you're out of oxygen you will now start your 5 minute countdown (make sure you're somewhere out of the way so no enemies attack you during this!). The Squil Syrup will regenerate your health while you suffocate, so it will prolong (or even halt, like it did with me) you dying from suffocation!
-Wait 5 minutes and you'll have your achievement!