kono meitantei Katsuragi Yako-sensei no!! この名探偵桂木弥子先生の！！ Of this famous detective, Katsuragi Yoko-sensei!!
She's a famous detective, because of her incredible detective skills, so she's addressed as a "master" of her craft.
The no の at the end turns the noun into a no-adjective, which normally qualifies what comes after it, but, in this case, it qualifies joshu, which is in a previous sentence.
sensei no joshu 先生の助手 Sensei's assistant. Assistant of sensei.
