Technically, the Quartet's first appearance was in episode #22 of SuperS. They are only shown as shadows, though. Their cue balls are in color, but the girls are only silhouettes. Zirconia tells them to get rid of the Amazon Trio, and PallaPalla summons the lemure Mr. Magic Pierrot, who tries to kill the Trio but is eventually destroyed by Sailor Moon.
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The Amazoness Quartet's first real appearance was in episode #23 of Sailor Moon SuperS. Serena, Darien, Andrew, Rini and her friend Melanie are in the arcade, and Momoko is talking about how she wishes that she were all grown up. The Amazoness Quartet girls are wearing dresses in their colors and watching JunJun play a video game. It's some kind of fighting game. JunJun says that it's really easy, but Andrew is amazed; he says that no one's ever gotten that high of a score.
The rest of the Amazonesses are watching JunJun play, when CereCere's bracelet beeps.
"We're being paged!" she says, and they walk out.
As they're leaving, they stop to tell Melanie not to be in such a hurry to grow up. They can't believe that she wants to be grown up, because when you grow up, you lose all your beautiful dreams. Then they walk out the door, saying "Don't dream that you're all grown up, big dreams are best just for kids" over and over again. Everyone else thinks that the quartet girls are a little strange.