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