Complete the game with 100% mission cleared.
Complete the indicated task after Chapter 4 to unlock the corresponding item for the Airship.
In order 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 completing 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.
At start of this battle summon at least one rank 2 water type Esper since all enemies are weak against water. Try a rank 111 Esper (peferably Mateus).
Once you've done so, begin 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 important to 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!
Have the goblin pouch equpid to Kytes during the mission with the material and at the end you will get 2 extra everburns.