Complete the game with 100% of the missions cleared.
After chapter 4, you can unlock various objects to decorate your airship with.
In order to obtain and view the Supreme Crest, complete every single side mission before starting the Final Chapter (about 97%).
After completing the first two levels in the Final Chapter, you should have 100% complete.
Create a new save file and then die during the boss fight. It will ask if you want to try again. Say no.
Go back to the airship and voila, you can apply the Supreme Crest to the airship!
||How to Unlock
||Obtain 1,000,000g or more
||Have a contract with 12 or more espers
||5% missions complete
|Ever-Summer Flower Bed
||Win 100 free battles or more
||45% missions complete
||Obtain 500,000g or more
||Obtain 100,000g or more
||25% missions complete
|Sparse Flower Bed
||Win 5 free battles or more
||Have a contract with all espers
||100% missions complete
|Viera Goddess Statue
||Have a contract with 25 or more espers
|Vivid Flower Bed
||Win 20 free battles or more
|Wings of Light Crest
||65% missions complete