Instructions
Synthesizing the Mythril Crystal
Go to any synthesis shop and speak to the Moogle in charge. Moogles are the white creatures with the pompoms on their heads. You'll find synthesis shops in most towns, Twilight Town, Radiant Garden, Port Royal and Agrabah to name a few.
Select "Free Development" from the synthesis menu to show a list of recipes. The required amount of items will display on the right hand side of the screen. If you already have some of the items, the amount in your possession will display next to each item.
Select "Mythril Crystal" and you will see that the ingredients are three Dense gems, three Twilight gems, one Serenity stone plus a Dense and Twilight crystal. If you have these objects, select "Synthesize" and you will receive a Mythril crystal after a short animation. If you do not have these items, you have to go defeat enemies to acquire them.
Acquiring Ingredients for the Mythril Crystal Synthesis
Fight against the Samurai enemies who roam in "The World That Never Was" on "Naught's Skyway." They have a chance of dropping the Dense Gem. Fight against the Berserker enemies in the same area to get the Dense crystal.
Fight against the Assassin enemies for a chance to get the Twilight Gems. Go to the top exit of Naught's Skyway to reach "The Hall Of Empty Melodies" where you will encounter Assassins.
Continue to the "Addled Impasse" area and fight the Dusk enemies for a chance to get a Serenity Stone. The Twilight crystal is dropped by the Sorcerer in the Nothing's Call area.
Return to the Moogle shop and synthesize the Mythril crystal from the ingredients you have gathered.