Tenchi Universe - Season 1 Episode 11 Time and Space Adventures Part I

Washu invents a dimension changing machine that allows its users to manipulate the world to their desires. Despite being forbidden by Washu from using the unfinished invention, the girls can't resist giving it a try, causing the whole family to be drawn into a maze of alternate dimensions where all their fears and fantasies are played out. The first story takes place in Heian era Japan, with Princess Ayeka as the fiancée of Tenchi, who himself is a bold warrior sent to defeat a legendary demon (who turns out to be Ryoko).