Select your character with Y instead of A to get alternate costumes.
Rock Lee
Complete the story mode without continuing, up to the fight with Zaibuzan. After you defeat Zaibuzan, Rock Lee will challenge you. Defeat him and you will be able to select him for all modes.
Sharingen Kakashi
After you unlock Kyuubi Naruto, complete the game in 1 player mode with him. Then, complete the game with Kakashi again. A message now tells you to press the Z or X button on the character select screen, when the cursor is over Kakashi to unlock Sharingen Kakashi.
Sound Test
Complete the game at once with all original characters in single player mode to unlock the sound test. Sound test can be found in the Omake menu (extras).
Unlock Kyuubi Naruto
After you unlock Rock Lee, complete the game twice with every character for the 1 player mode. After this is completed, a message will tell you to press the Z or X button on the character select screen over Naruto to get Kyuubi Naruto. You will hear a roar confirmation.
Unmasked Haku
Successfully complete the game in arcade mode as Zabusa under difficulty setting 3. Then, highlight Haku at the character selection screen and press X or Z.
Alternate Costume...