Army of Ruin

Earth is the leaf icon on the trinkets, so for this achievement, simply completing the stage without picking any earth element trinkets. It's naturally in your best interest to prioritize weapons that don't use earth to evolve, such as Wolf's Fang and Mystical Firecrackers, but this is what makes this a bit of a challenge: so many good/starting weapons use earth to evolve, like the Ranger's Bow with Ker, the Necromancer Gauntlets, the Wolf's Fang with Ogol, Toxic Stench, etc. Stick with weapons such as Metoerite Blast, Landslide, Whirlwind Axe, Golden Trident, Storm Javelin, etc.

As a side note, having at least two Rerolls available helps here too, just so you don't get screwed by "bad" RNG into being forced to choose an earth element trinket at some point.