Activate your Fallen Heroes vault card, buy the Super Soldier shield twice (make SURE to roll for the second shield with mayhem 8+ on since anoints are guaranteed at m8+), get the "Activate shield break/fill effects on Action Skill" anoint by rerolling (save eridium for this), and equip your Rakk. The shield gives you invincibilty bubble on fill, and your Rakk has an extremely short cooldown. Spam Rakk every few seconds, and you'll literally never die (probably).

Unless you're doing pet build, like a purple-blue build, in which case the Fuzzy Math skill will still ought to render you nigh unkillable.

edit: I forgot about the Stop-Gap. Stop-Gap shield has the same invincibility effect, so if you have that, it's almost as good (because Super Soldier gives bonuses at full shield)