Unlock the following items for the airship by performing the corresponding tasks after Chapter 4:
AIRSHIP DECORATION - HOW TO UNLOCK Ald Fountain - Get at least 1,000,000 gil. Arawashi's Statue - Have a contract with at least 12 Espers. Copper Crest - Complete 5% of the missions. Ever-Summer Flower Bed - Win at least 100 free battles. Golden Crest - Complete 45% of the missions. Granite Fountain - Get at least 500,000 gil. Marble Fountain - Get at least 100,000 gil. Seraphic Crest - Complete 70% of the missions. Silver Crest - Complete 25% of the missions. Sparse Flower Bed - Win at least 5 free battles. Stuffed Tomato - Have a contract with all the Espers. Supreme Crest - Complete all side missions to reach 97% before starting the Final Chapter. Completing the first two levels of the Final Chapter to get 100% mission completion. Save the game on a new file and intentionally die during the Boss fight. Answer "No" when asked to save again then return to the Airship and the Supreme Crest will be unlocked. Viera Goddess Statue - Have a contract with at least 25 Espers. Vivid Flower Bed - Win at least 20 free battles. Wings of Light Crest - Complete 65% of the missions.
To forge all weapons in Cu Sith's personal "Everburn Essentials" set you need 5 bars of Everburn. You can get two of these by finishing a side quest available in Chapter 7. The material description lists the Skysea as a location where you can find the remaining Everburn. This is simply not true. The only other place you can get Everburn is in the Area "Gates of Darkness" available after Mission 1 in Chapter 9. Each time you complete the summoning melee you get one (or more) bars of Everburn. Unfortunately by that point in time, Everburn weaponry is inferior to alternatives.
The Ring of Pacts features a set number of slots for Espers that you can purchase. Some of the slots are blocked with stones; these disappear as you progress and you can buy the Espers with Auracite. However, there are hidden slots for the very powerful Gilgamesh and Zodiac, which can be unlocked by completing Chapter 9 sidequests, and the mediocre Famfrit Esper, which can be unlocked by completing Chapter 7 sidequests. Sephiroth2.2
When this battle begins, summon at least one rank 2 water type Esper since all enemies are weak against water. Try a rank 111 Esper (peferably Mateus). After that, start by closing off the two summoning gates on the right (kiling enemies as you go along). When you get to the top gate you will fight Chaos; use the spell Blizzaga and have Penelo cast Cure on your troops. With that location seized, it should be easy to send a wave of fliers across the lava towards Mydia. Summon more fliers to attack her when the other opposition is suppressed. It's vital that you know that Mydia will remain immobile as long as you do not approach her from the ground. Hence, the fliers you use to mount the attack will pretty much defeat her without you having to worry about being counter-attacked.