Here is the full list of all 24 Beyond Reality achievements.
Defeat the Final Boss on Hard Difficulty
Reach Level 10 With All Possible Party Members
Defeat the Final Boss Without KOs
Defeat the Final Boss on Expert Difficulty
Defeat the Final Boss
Reunite the Group
Obtain the Three Legendary Weapons
Complete the Chronicle
Defeat 8 Bosses
Defeat 4 Rare Monsters
Defeat the Desert Snake
Defeat the Lord of the Winds
Defeat the Ancient Demon
Defeat the Wirewolf
Defeat the Man-Eating Plant
Defeat the Ice Pixie
Defeat the Fire Pixie
Defeat the Three-Headed Wolf
Defeat the Wyvern
Make an Offering
Defeat the Unicorn
Defeat the Expert Thief
Defeat the Iceshackle Cyclops
Survive an Explosion