The following are Komas that can be unlocked from doing something other than beating J-Adventure mode missions. The easiest way to get the "Battle [number] times" Komas is to repeatedly fail the "get hit once and you lose" missions in J-Adventure mode.

Ichigo Help Koma: Get 450 Koma
Ichigo Battle Koma: Get 540 Koma
Vegito Battle Koma: Get all Koma
Goten Help Koma: Battle 200 times
Bobobo Battle Koma: Battle 350 times
Naruto Battle Koma: Battle 400 times
Don Pachi Battle Koma: Battle 450 times
Sasuke Battle Koma: Battle 500 times
Kakashi Help Koma: Draw a Konoha leaf emblem in the upper right part of the touch screen during the introduction sequence. Alternately, get 360 Koma.
Sakuragi Help Koma: Draw a basketball shoe in the lower left part of the touch screen during the introduction sequence.