Start a new game in Survival mode, and ensure the game difficulty is on either Normal or Easy. Peaceful turns mobs off.
Wait until night time and the enemy mobs will appear - simply kill a spider, creeper, skeleton or zombie with a wooden or stone sword and the achievement will unlock!
You can also import your saves from the Xbox One version and gain other achievements along the way. Another useful trick is to go to the X1 version, load up and save a Tutorial world, and import it to the new beta.