Penguin-sensei is an animal coach who teaches Coach Mascots and Pair Charms at Pretty Top, and is strange just like Yamada Yamao. He is always accompanied by him and is always scratched by the pair charm Vivvy.

(Source: Pretty Rhythm Wiki)

Naru Ayase is an 8th grader who can see the colors of music when she listens to it. For Naru, who is extremely good at decorating, becoming the owner of a shop like Dear Crown was her dream. One day, she finds out that the manager of a newly-opened shop is recruiting middle school girls who can do Prism Dance, and immediately applies. Naru begins to Prism Dance at the audition, and an aura she's never experienced spreads out in front of her. At that moment, a mysterious girl named Rinne asks her if she can see "rainbow music". 
(Source: Anime News Network)

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Prism Stars are performers on the new popular ice show, Prism Show. They are superidols whose techniques, singing and fashion sense are a cut above all others. Aira and Rizumu are two Prism Stars whose goal is to become the best, the Prism Queen. However, the road to success is bumpy. 
(Source: AniDB)

Three years after the events of "Pretty Rhythm: Aurora Dream," Aira, Mion and Rizumu have grown up and tutor a new group of aspiring idols: Karin, Reina, Mia and Ayami, who form the Prizmmy&#9734;. Teenage girls from Korea, named Somin, Shiyoon, Haein, Chaekyung and Jae Eun (who are the PURETTY), appear as a rival group. 

The new Pri☆Chan Land amusement park has opened near the Prism Stone shop. It is a semi-virtual world where the mascots of idol teams come to life, and even perform as idols themselves. Park manager Meganii announces the Illuminage tournament, where idols compete to become princesses of each area of Pri☆Chan Land, and at the finale one team will be chosen as Illuminage Queens. With the help of their mascots, Miracle☆Kiratts, Meltic StAr and other teams compete to become the Illuminage Queens.
 
(Source: Anime News Network)

The film will compiles Prism Show scenes from all three television anime series.