For this achievement you'll to have active the Healer Shrine which activates when the Healer trait is lvl 2, needing 4 Healers in play. Engineer Turret and Shaman Totem activate at trait lvl 1, which require 2 Engineers and 2 Shamans, respectively. As none of those traits share units you'll need a total of 4+2+2=8 units which is impossible. That means we'll need 2 banner. So for this reason you'll start with the character Thokor and restart your run until you get a Healer banner. After you get the banner, play the game normally going for 3 Healer units and either 2 Shamans/1 Engineer or 2 Engineers/1 Shaman. For the last Shaman/Engineer you'll need to acquire a the "+1 army size" trait and having in your team 3 Healers, 2 Shamans and 2 Engineers, with the Healer banner equipped to a Shaman or the more consistent strat, buying a Shaman/Engineer banner from the shop. This is simple: take the combats that give you the most gold and when you get to a shop hope that you get the banner that you need.
Remember this achievement requires a combat win not a full run win. (also play on the easiest difficulty)