Save Scum method has now been patched. The only way of getting this currently is to complete the game on Armageddon difficulty from the outset. I'll leave the old save scum video attached for anyone interested in how that was done.
This achievement may also be falling victim to the tracking bug wipe. A lot of people are reporting finishing the game on Armageddon and it still not popping! It's unrealistic to assume you can finish the game in one sitting to get this.
Note: I couldn't get this achievement to pop with the weak ending (Option #1). It needed to be done on the true ending (Option #2) where you fight the Twins. You only need to kill one Twin to defeat them both. I suggest fully upgrading the "Fat Boy" and it should take 5-6 rockets to kill one of the Twins.