Hard West Ultimate Edition

Note: After i wrote my solution, i found a few more infos about the achievement on steam. Haven't fully verified it myself although what is written there does make sense from the wording of the achievement. Credit goes to the folks in the steam forums for that.
There are basically 2 ways to complete this achievement.
1. You can attack and kill enemies, just not with anything that involves shooting. So you could complete a fight with consumables or non-shooting abilites like Shriek, Equalisation or the Shadow attack only. But since abilities mostly cost luck and consumables are used up, you might run out of resources before you killed all enemies.
2. Use one of the few encounters that can be completed during preparation phase without killing/fighting. I know of 2: The Aspirton bank robbery in "As Good As Dead" and the mission where you have to free the reverend in "Graveyard Shift".
This is what I did and what i'm going to explain further down.

How to unlock during Graveyard shift
Character loadout:
1. One character must have his heat level as high as possible. Also, movement bonuses help greatly. Movement bonus example: Pair of Queens (2x2 +4 pair bonus) + Snakeskin boots.
2. Any additional character should have low heat. Unequip any secondary weapon and use only a low heat weapon as primary.

Execution
The high heat character should make hist way to the star-shaped target. Keep threatening the boss until the other character(s) has managed to free the reverend AND all but the high heat char have made it to the exit zone without alerting anyone. Then stop threatening the boss and just book it, run to the exit. With sufficiently high threat and movement you should easily be able to reach the exit before the boss raises the alarm.

Note to german players:
The german translation of this achievement's description is completely wrong. Completing just a single fight without shooting is enough, you do NOT have to complete ALL fights without shooting.