Complete Stage 36 (Ichigo vs. Ulquiorra) to unlock Stage 37 (Throne Room) and defeat the boss, Aizen.
Hollow Ichigo (Horned) form
Complete stage 36 (Ichigo vs. Ulquiorra). Then, equip Ulquiorra as a supporter and link with Ichigo. Press L to change forms into Hollow Ichigo (Horned).
Released Ulquiorra form
Complete stage 36 (Ichigo vs. Ulquiorra). Equip Ichigo as a supporter and link with Ulquiorra. Press L to change forms into Ulquiorra (Released).
Stage 36
Complete all maps 100%.
Ulquiorra Second Release form
Complete stage 36 (Full Hollow Ichigo vs. Ulquiorra Second Release). Equip either form of Ichigo as a supporter and link with Ulquiorra (as you). Press L to change forms into Ulquiorra Second Release.
Unlock Kon
In the Real World Challenge, at map # 13 follow the hell butterfly to the hidden door between the first and second candle sticks, which will lead you to Ichigo's room where Kon is waiting to fight you (and "conquer" the world). Defeat him and you'll unlock Kon.