This achievement cannot be earned until post-game.
Additionally, you will have needed to keep the Emblazoned Sword given to you by Sigmund early in the storyline, as it is a unique item, and required for the synthesis.
Edward will be doing this IC, and he needs to be at IC level 6 (which will get you the Claridian Hammer achievement). Once you enter the Seraphic Gate in post game, a number of new synthesis recipes automatically unlock, including the Azureal Blade.
1. Emblazoned Sword x1: Storyline item. Do not sell.
2. Amarlista x2: Can be farmed from Flying Swords in the Castle Valette section of the Seraphic Gate. If you downloaded the "A Voucher", these can be bought at any store.
3. Gram x1: This is a sword that must be forged by Edward.
To synthesize Gram, you need:
1. Atlantis Metal x3: Can be farmed from Hill Gigas in the Graad Woods section of the Seraphic Gate. Available at any shop with the "A Voucher".
2. Quartz x1: Can be farmed from Storm Gigas in the Luce Plains section of the Seraphic Gate. Available at any shop with the "A Voucher".
3. Aqua Blade x1: Buy it at the Port Zala weapon shop for 25,000 fol.
(Quartz can also be synthesized by Seraphina and the Aqua Blade can also be synthesized by Edward)
Before attempting the synthesis, SAVE YOUR GAME. You only have one shot at this, and you CAN FAIL.
Upon successful synthesis, the achievement will pop. Immediately equip on Capelle for best results. :)
Thanks to Crimson Drifter for recommendation to include Gram's synthesis ingredients.