This should come naturally as you progress with Silent and a turtle deck setup (prioritizing block/poison over front-loaded damage). Poison is obviously going to be necessary, Noxious Fumes is probably the easiest here as it does apply to all mobs. Now, on a multi-mob floor level (or boss if you're deck can handle it) build up a nice defense (ie couple of Footworks in place, easily meeting block needs each round) and get your Fumes into place asap. Once this scales up and you win, achievement will pop. Probably easiest against mobs that don't themselves scale. Mobs don't all need to die on the same turn.
Things to keep in mind. Poison must deliver the killing blow. You can deal damage directly to the enemies so long as poison deals the final damage. Caltrops should probably be avoided as killing with this damage will void the achievement.