When you enter a fight with one of the enemies, you will have a variety of power ups at your disposal, such as healing orbs and spears as well as a buff which ignites your sword with flames for additional damage.
I managed to achieve this when fighting Rhodes - while I was at low health, I activated the flame sword buff and died from it being active, unlocking the achievement.
iMaginaryy adds that the death needs to be due to health decay, meaning if the enemy takes your life the achievement will not unlock!