This can be unlocked as early as Mission 1, 'Harbin's Dig Site'. This must be done within one level.As you make your way through the level, you may find a red health potion bottle here and there. Be sure to pick them up as needed, but you can only hold one at a time. When you reach the final sarcophagus room, as you kill enemies, they drop health potions. Pick up any remaining potions and drink them to unlock this achievement.
This also can be done in Horde. Note that when you pick up a health potion, it will eventually respawn but may take several waves to do so. Hopefully you can survive that long.