Unlock Hard difficulty for that character:
With any character beat the game in Story mode, Normal difficulty.

Unlock First Picture:
To unlock their First Picture beat the game in Story mode, Normal difficulty with any picture.

Unlock Second Picture:
With any character beat the game in Sudden Death to unlock their second picture.
Unlock Third Picture:
With any character beat the game in Story mode, Hard difficulty to unlcok their third picture.
Unlock Group Picture:
With all eight characters beat the game in Story mode, Normal difficulty.

Unlock Nyamo:
With Yukari beat the game without continuing in Story mode, Normal difficulty.

Unlock Yukari:
With Tomo, Osaka, Yomi, Kagura, Chiyo and Sakaki beat the game in Story mode, Normal difficulty.

Unlock Audio Clips for that character:
To unlock Audio Clips beat the game with any character in Story mode, Normal difficulty.
Unlock BGM in the Omake Section:
With all 8 characters beat the game.

Omake sounds:
As any character successfully complete the game in Normal difficulty setting.

Omake background music:
With all characters successfully complete the game in normal difficulty setting.