Bonus characters - Defeat one of the following characters in the indicated chapter in Story mode to unlock them:

Aaroniero: Defeat in Chapter 27
Aizen: Defeat in Chapter 49
Grimmjaw: Defeat in Chapter 10
Ichimaru Gin: Defeat in Chapter 47
Nel (Adult): Defeat in Chapter 41
Noitora: Defeat in Chapter 26
Shinji: Defeat in Chapter 3
Szayel: Defeat in Chapter 32
Ulquiorra: Defeat in Chapter 29
Yami: Defeat in Chapter 6
Zomari: Defeat in Chapter 36

To unlock Filler Captain Amagai, earn money in Story mode, Survival mode, and Two Player Versus mode. He can then be purchased at Urahara's shop at random.

Moves

Dash or Shunpo: Press C.
Counter: Press Z.
Strong attack: Press B.
Weak attack: Press A.
Slash combos: Shake Wii-mote.
Special strong attack: Press Z + B.
Special Weak attack: Press Z + A.
Bankai: Press Z + shake Nunchuck.

Additionally, the following moves can be done in Team Battle mode on the Wii-mote.

Switch with your partner: Press Up.
Summon your partner to attack briefly: Down.
Summon CPU-controlled partner to fight with you: Z + Down.

Some characters can also do a special move by pressing Z + shake Nunchuck twice:

Ichigo: Hollow Mask
Byakuya: White Imperial Sword
Grimmjow: Death Gallon