Here is the full list of all 42 Ray Gigant achievements.
You defeated the Gigant, Pendragon.
Relaxed with Conner at the pub.
You defeated the Gigant, Loki.
Your first entry to Holy Rock.
You defeated the Gigant, Asura.
Gained power recognized by the Yorigami.
Went on a hot springs vacation with everyone.
You defeated the Gigant, Huanglong.
Entered the other dimension for the first time.
More commands set for diversity in battle!
You defeated the Gigant, Nine-Tails.
You gained a stronger version of the same equipment.
Your first access to the power of the Yorigami.
You entered the Megalosite for the first time.
Ichiya Amakaze transferred to the Academy.
Thanks for playing through to the end! Until we meet again!
You defeated the Gigant, Brahms.
Arrival into an island that isn't much of an "island."
You defeated the Gigant, Tescalia.
Came in contact with a mysterious new Gigant.
You defeated the Gigant, Lilith.
You defeated the Gigant, Uroboros.
Arrival onto the aerial mothership, Artemis.
Your first entry into the Gigant Shrine.
You defeated Ray Gigant!
Gained power fit to command the powers of the Yorigami.
Ichiya Amakaze learned all his commands.
Kyle Griffin learned all his commands.
Nil Phineus learned all her commands.
You let go the power you gained.
You gained a very powerful weapon.
You gained a very powerful shield.
You gained a lot of accessories.
You gained various amounts of foods.
You can't eat any more.
You fought until your stomach growled.
Over kill your enemy with SBM.
You mastered the art of timing through SBM.
You destroyed all the enemies in a sector.
That was quick. The enemies were no match to you.
Your first experience of Parasitism.
You're getting a bit too used to using Parasitism...