The question is, who is this mermaid supposed to be?
She appeared in episode fourteen of Dragon Ball as well as an early chapter of the manga, I believe. She was just a one-off character during Goku's early training days under Roshi. As much as it seems to imply mermaids are part of the canon Dragon Ball universe/setting, she's the only one seen or referenced.
Though, Roshi was wearing a tuxedo with his turtle shell when he met the mermaid in the canonical appearance.