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