Cuphead

Got it in first try in the level "high-noon hoopla" (the level is a cactus in the south).
There's only one minion and its super easy to avoid them. its in the first stage. a minion that shoots spikes will ONLY appear in the place where doesn't have the cowboy, so just dodge your shots so it doesn't hit him. when you defeat the first stage without killing any minions, just play normal until you kill the boss and the achievement will be yours

Edit: Here's a video by BearlyComplete to complement the guide.
Full credits to him!
Link:
Edit: Also, this can be done in the simple difficulty. Credits to maka for saying that!

Inkwell Isle IV
Level: High-Noon Hoopla
Difficulty: Simple

There's only 1 enemy type in this entire stage that is considered a "minion" and it is a horse that comes across the screen and launches a cactus ball at you. If you can get past the first phase without killing any instance of this enemy, and then complete the level, the achievement will unlock.

Also, this can be done on Regular difficulty too, but Simple has 1 less phase and is therefore easier.

This achievement can be done easily on the level “High Hoop Hoopla” I think (it’s the cactus on Inkwell isle 4) do on simple difficulty. There’s only one kill enemy that easy to avoid. They are these donkeys that can spit out Cactus balls. Avoid killing them. After you get the knockout the achievement is yours my friend!