How do I obtain Fine Alcrysts?
According to this page, aside from King Mog event, you can obtain Fine Alcrysts by
Crafting
20% chance to obtain one after crafting any ability (source).
Trophies
Silver for Fabled Smith, Divine Technician, and Peerless Chemist.
Reward
(Event) Lunar New Year - Nian Beast Challenges! - INT (Day 5)