Ive found 2 classes that work ok? at getting this achievement. The goal is to complete a level without dealing any damage as any classes. This includes selling your heros and only dealing damage as the king. It wants all bars at the end of the level screen for damage to be 0.You can do this as early as the 2nd level. Start off by picking the new Hero Oni or Deep Cultist.

For the first level, just clear it. While in the shop, before the 2nd level. You want to buy a identical hero to the one you first bought. By having 2 of the same hero's. We will get there bonus traits/skills. You can limit what hero's spawn at the start of the game before picking your run, But theres still a minimum of 12 heros required. a restart here is required if you cannot buy another version of your hero.

Cultist
When you start the 2nd battle and are going for the achievement. You want to keep as far away from enemies as possible. The battlefield will be litterd with hooks that deal 10dmg. 2 hooks will kill a enemy. Theres more than enough there to clear the stage. You just have to keep on running around and luring enemies in to them. If a Cultist summons there tentacles, its not round over, just keep on moving. They will not be able to attack if a cultist cant order them to attack a enemy.

Oni
I personally found this hero to be the easier, but more time consuming method. When you have 2 of these new heros, there bonus is to drop down a red arch. It will deal 10dmg, but it wont go away, until you run underneath it, then it will repeat maybe 5sec later. Once you get in a rythem of looping the stage with enemies following behind you, you just keep on looping but hit a red arch on your way and keep your distance.

Congratulations, Whats your reward? Nothing. Have fun!