From Pikipedia, the Pikmin wiki
The Mirrored Stage (ミラー・ステージ?, lit.: "Mirror Stage") is a treasure found in Pikmin 2. It is actually a powder case. It is located in the third sublevel in the Shower Room. It is found inside a Greater Spotted Jellyfloat. Defeating the Lesser Spotted Jellyfloats and other enemies will make it easy to retrieve it from the larger Jellyfloat.
An interesting thing to note is that the "mirrored" part doesn't provide a mirror effect, but is simply a black wall. Producing such an effect could be complicated, so Nintendo worked around it by exploiting the game's camera. In the Treasure Hoard, the camera cannot go lower than a certain level, and it is unlikely that a player will take the time to hold / in the story mode to look underneath the lid.
“Every day, it's nothing but work, work, work. Sometimes I need to just get it off my mind. So, I set this thing up as a stage and taught the Pikmin a song-and-dance routine. Red, purple, white, yellow, and blue Pikmin danced in perfect unison and sang their little hearts out. When I return home, I should take up a career as a dance instructor.”
“Come rain, wind, or typhoon, this stage will always support the hidden singer deep in your soul. It is a lovely instant dance stage. How about taking one on tour with you, star of rock?”
Pikmin 2 website
"This wonderful instant dance stage that will always support the hidden singer deep in your soul. Just the thing for entertainers."
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