For clarification: In Strange Brigade, if you die while owning a health potion, you do not have to restart at the last checkpoint. Instead, you are being put in a sarcophagus, which you can escape by consuming your health potion.
Since one can carry only one health potion at a time and this achievement requires players to escape a sarcophagus five times without actually dying in between, my strategy on obtaining this achievement was simple:
1.] Find a potion, and keep it until you find another one
2.] Upon locating another potion, kill yourself (grenades & traps), or let enemies kill you
3.] Drink your potion in order to escape from the sarcophagus (
4.] Pick up the second potion you just found, keep it, and find another one
5.] Rinse and repeat
By doing it this way, you can considerably lower the risk of dying while not carrying a potion, which would reset your streak. It goes without saying that going for this ach on Normal or Easy difficulty lowers the risk of dying without wanting to, especially considering your health does not get replenished upon exiting a sarcophagus.
Personally, I did it on Cut-Throat Caverns, on Normal difficulty. There are plenty of health potions scattered throughout the level, though any other mission probably works just as well.