The Lord of the Rings: Adventure Card Game - Definitive Edition

You will earn this naturally as you work through the other achievements in the game. Note that for this achievement, spiders and orcs (which include goblins) do NOT count. Snakes, bats, birds, etc. all DO increment the counter for this achievement. If you inspect the card of an enemy, it needs to say “Creature” on the bottom to count. Also, it appears that kills from guard actions (where they attack a unit in guard and die as a result) and Legolas’s hero action (doing one or two damage in Upkeep) do not count toward this.

While there is no in-game counter, the achievement progress does increase if you look at it via the achievements tab on the Xbox dashboard, so you can get an idea when you are close to unlocking it.