Here is the full list of all 40 Relic Guardians: Complete Edition achievements.
Finish the prologue episode
Finish the first episode
Finish Black's briefing
Finish the Stone Age episode
Finish the Babylon episode
Finish the first interlude episode
Finish the Egypt episode
Finish the Phoenicia episode
Finish the Persia episode
Defeat Alch on Story Mode
Finish the Greece episode
Finish the second interlude episode
Finish the Japan episode
Defeat Timage on Story Mode
Defeat Rock on Story Mode as Wizz
Defeat Alice on Story Mode
Defeat Kaiser on Story Mode
Defeat Twisted Kaiser on Story Mode
Finish the full Story Mode
Beat Kaiser as Black on Story Mode
Finish the Tutorial... please
Get at least one of each item on Arcade Mode in a single run
Click 40 times or more on the SP Tie Breaker mini-game
Charge a x9 ATK in one battle
Defeat an enemy with one single ATK as Helm
Defeat Alch Phaser on Arcade Mode
Defeat Eric "Timage" Warden on Arcade Mode
Defeat Rock Palentis on Arcade Mode
Defend against Alch's SP on Arcade Mode
Beat Timage with full HP on Arcade Mode
Land an SP on Rock on Arcade Mode
Defeat Alice Beauchamp on Arcade Mode
Defeat Kaiser on Arcade Mode without using any Ankh
Finish Arcade Mode as Wizz
Finish Arcade Mode as Shakal
Finish Arcade Mode as Helm Watch
Finish Arcade Mode as Stalph Trigger
Transform Wizz into her Awoken Seed form on Arcade Mode
Finish Arcade Mode without using any items in a single run
Achieve the S rank