No Need for Princesses!

Tenchi Universe – Season 1

Princess Ayeka, first princess of planet Jurai, regrets responding to Mihoshi's distress beacon when she meets Ryoko on Earth. The two of them go back a long way, and have been enemies for years. During her time on Earth, Ayeka finds herself falling for Tenchi, and cannot endure Ryoko's shameless flirting with him.