Successfully complete one of the indicated tasks to unlock the corresponding character:

Byakuya Kuchiki: Successfully complete "Byakuya's Cooperation" in Free Time mode. Alternately, defeat him in Bleach tower, Level 9.
Gin Ichimaru: Defeat him in five turns (before Izuru) in Bleach Tower, Level 6.
Hanatarou Yamada: Successfully complete "Hanatarou's Cooperation" in Free Time mode. Alternately, defeat him in Bleach Tower, Level 7.
Hinamori Momo: Successfully complete "Hinamori's Cooperation" in Free Time mode. Alternately, defeat her in Bleach Tower, Level 8.
Izuru Kira: Successfully complete "Izuru's Cooperation" in Free Time mode. Alternately, defeat him in Bleach Tower, Level 6.
Kaname Tousen: Defeat him in Bleach Tower, Level 12.
Kusaka: Have Hitsugaya defeat him, and successfully complete Bleach Tower, Level 21.
Renji Abarai: Successfully complete "Renji's Cooperation" in Free Time mode. Alternately, defeat him in Bleach Tower, Level 9.
Retsu Unohana: Successfully complete "Unohana's Cooperation" in Free Time mode. Alternately, defeat her in Bleach Tower, Level 7.
S. G. Yamamato: Successfully complete "Yamamato's Cooperation" in Free Time mode. Alternately, defeat him in Bleach Tower, Level 4.
Sajin Komamura: Successfully complete "Komamura's Cooperation" in Free Time mode. Alternately, defeat him in Bleach Tower, Level 10.
Shaolin Fong (Soi Fon): Successfully complete "Soi fon's Cooperation" in Free Time mode. Alternately, defeat her in Bleach Tower, Level 5.
Shunsui Kyoraku: Successfully complete "Kyoraku's Cooperation" in Free Time mode. Alternately, defeat him in Bleach Tower, Level 11.
Shuuhei Hisagi: Successfully complete "Hisagi's Cooperation" in Free Time mode. Alternately, defeat him in Bleach Tower, Level 12.
Yoruichi Shihouin (Current): Successfully complete "Yoruichi's Cooperation" in Free Time mode. Alternately, defeat her in Bleach Tower, Level 5.
Yoruichi Shihouin (Former): Defeat her in Bleach Tower, in the level she is in with Kisuke Urahara.