Mission data is
[1)Spirit which you will use] VS [2)Opposing character's name]
[3)The mission objective] [4)The reward for completing objective]
Rewards can be of two types: time bonus - adds the time to timer; life bonus - replenishes part of your lifebar.
You can also replenish your lifebar during fights via healing items such as sushi.
After 1st mission select screen where you selected your mission, you are presented with 99 seconds on timer, and with full lifebar. After a fight you will be transported to next mission select screen. If you completed mission objective, you will be presented with your reward bonus to lifebar or timer. Rewards are crucial because you will lose when you either run of time or of lifebar, so you wont be able to complete survival mode (its possible to complete it, you fight nearly all characters, then bosses and Demon Gaoh is the last opponent. Dont remember do you fight Kuroko there or no though..)
Because everything is in japanese, I translated mission objectives / rewards to english:

