Through expeditions, you should easily find some psychedelic mushrooms. Feed them to one of your survivors until they are hallucinating. Now send this survivor on an expedition by themselves and they should immediately hallucinate, causing either the "Torn Yurt" or the "There was a cat that really was gone" event to occur, unlocking the associated achievement. Pause the game and return to the main menu; then continue your game and rinse and repeat until you trigger the other event to occur and earn both achievements.
See the video below for more information.