Hard West Ultimate Edition

The Aspirton Bank Robbery is a marked side quest that will unlock during the course of the main story of the scenario. For this achievement you have to select robbing the bank during the day.

However, the achievement's description is a bit misleading.
The moment the preparation phase ends and combat starts, a bell will toll, starting a timer for demons to appear.
From the description, one might assume that, even after the bell, the achievement can still be obtained by completing the fight before the timer runs out.

That does not work, however. I've tried multiple times.

The moment you can hear the bell, the achievement can not be obtained anymore. That means you must finish this mission in the preparation phase without ever starting combat.

I'd suggest you gear your characters towards a low heat, high movement setup. But you should also bring one high heat character to subdue the bank director. If you also give that character the Disguise ability, he can even walk in through the front door. If you have issues with obtaining that card, restart the scenario with the 'all cards unlocked' gameplay mod enabled.

Make your way to the bank director with at least 2 characters. At least one needs to go the 'long way around': to the telegraph and from there through the backyard and back door of the bank. Subdue the guard in the back, then the director, rush to the safe, done.