The Kitsune's dance is the very same each time she performs it, and you have to look for possible anomalies 8 times in a row. A failure forces you to restart from the beginning of your playthrough.
An automatic saving system registers the apparitions (the creatures which sometimes copy the Kitsune's appearance during dances) you already found in the Apparition Encyclopedia. In order to get 100% achievements and unlock the end of the game, players need to complete this encyclopedia.
However, this saving system is confusing : it seems that the Apparitions found during a lost playthrough may not be registered. This may be frustrating, since some of them are rare and/or not so easy to discover.

For these reasons, you need to check as many details as possible during each step of the dance. I recommend you to procede this way :

1) Close-up on the Kitsune's face : Check her eyes, her hair (length and colour), the presence of the red ornament and the fox mask on her head, the look of her ears, her collar and the magatama on it, and the presence of possible new details (ex : mole).

2) Ascending close-up on the Kitsune's feet and dress, until reaching her face : Check the kitsune's shadow (it may not be there, or have a different form), her feet and legs, dress (colour, length, design), the sleeves, cleavage, hands and fingers. Don't forget to check her thighs, shoulders and arms : small anomalies may also appear there.

3) When the Kitsune takes a lowered posture, doing a « shush »sign, turn the camera to the right side, until you can see her armpit. A discreet apparition may be there on her breast. Right after this, return to the initial position of the camera.

4) When she is raising her right arm, while closing her eyes, the Kitsune is about to turn around. Be ready to check her panties (this is for the purpose of spotting apparitions, I swear!) at this very moment, since you won't have a lot of opportunities to do it after this.

5) A few seconds later, the Kitsune's fingers will be touching, in a gesture which looks like a heart. Focus on this sign, it may not be the same everytimes !

6) After this, you have a few seconds to check her back. Be careful about the purple ornament on the back of her head, her fox tail, the paper strips,.. and most of all, the short white cloth covering her back. This last detail is easy to forget, and her hair may prevent you from checking during some steps of the dance.

7) When the Kitsune's is doing a « fox sign » with her two hands, make sure she does it right.

8) Check the two fans that will materialize in her hands.

9) After the fans disappear, check the environment : sky, moon, size of the stage, the Kitsune's shadow, … until the end of the performance.

Note : Depending on the number of stars attributed to each anomaly in the Apparitions Encyclopedia, some anomalies won't occur while playing in the first difficulty setting. After completing your first playthrough, it is highly recommended to switch to Fox's Trial difficulty.