Ailic's Stranger

wants to make his own. He wants you to find parts for him.
 * Intact GL Ball
 * Intact BL Ball
 * Intact LV Ball

The Intact Balls are not physical Items in your inventory, they re just quest updates. In order to get these, you need to find the Broken Balls and inspect them to start the three sub-quests which, although they are NOT listed in the rewards, will give you the quest updates. Each of the three says only that it rewards 1,221,300 XP, 122,130 TP and. All three are completed by talking to.
 * Item: 
 * - Get the following parts:
 * from
 * from at
 * from
 * Item: 
 * - Get the following parts:
 * from
 * from
 * from at
 * Item: 
 * - Get the following parts:
 * from
 * from
 * from at

I can verify, you get all three balls after looting the tenth for.