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, the RNG will eventually give you the option for Barrels. Search them to find a mask and wear it. More RNG required, but eventually you'll get an option for Hut. Select this and choose Disguise for the achievement.
Note: you can keep going after this for the Extinction achievement. Please see my guide there for more information.