Extra missions can be found at the "Missions" stations.
Extra missions provide extra battle scenarios. The only ones of actual consequence will be your "Limit Breaker" missions, which will allow you to continuing leveling up your characters.
The first "Limit Breaker" mission will appear once your custom character reaches around level 16 or 17. This mission will net you both the achievement and allow you to level up characters past level 20.
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