Dimensions has three different worlds you can travel between: Desert, Groundhog Day, and Jungle. Upon waking up you will get the option for Portal, which will have an RNG option each run of the game. Roars will take you to the Jungle, and Wind will bring you to the Desert. At some point within Desert or Jungle you will get an option for Portal again, which will take you to the Groundhog Day Dimension.
After entering the Jungle, you will eventually come to a Campfire where you can select an option for Chieftain. Talk to him, choosing either option several times (doesn't matter which) until you get a Spear and Armour. Now you're at the mercy of RNG again, but eventually you'll get an option for Ants. Choose to Fight them for the achievement.