Brotato

This achievement is a bit of a pain, because there are two ways to get Curse:
 

• Buying a Cursed item/weapon from the shop
• Killing a Cursed loot alien

For the former, this is really easy to avoid but they are clearly marked as increasing your Curse, and if a weapon is Cursed it has a pretty obvious purple swirl over the weapon's image. It's the second point that is a pain. Randomly during a run, a loot alien could show up that is Cursed, and if you kill it, you get +1 Curse, voiding this achievement on that run. There is no way to reduce Curse, that I'm aware of. The Cursed loot aliens look similar to the normal ones, except they have on a purple backpack and look slightly different. I have a screenshot below showing the Cursed loot alien over on the right side of the screen.

The issue is that even if your turrets, mines, etc, kill the Cursed loot alien, you get +1 Curse. This makes it really easy to accidentally kill one without even realizing it if you're playing with accessibility settings and are one-shotting all enemies. The most reliable way I've found to do this was to use a melee build and stay in the center of the screen. In general, loot aliens won't come toward you. They tend to run away and hang out around the outside of the arena once they spawn. However, just pay close attention because during my successful one I saw a Cursed loot alien start creeping up toward my area of melee attack during Wave 19 and almost ruined the whole thing. Be careful about increasing your Range too much because of this (you might accidentally kill one before you notice it).