Here is the full list of all 24 Beyond Reality achievements.
Defeat 8 Bosses
Defeat the Fire Pixie
Defeat the Ice Pixie
Complete the Chronicle
Defeat the Three-Headed Wolf
Defeat the Final Boss on Expert Difficulty
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
Defeat 4 Rare Monsters
Obtain the Three Legendary Weapons
Reunite the Group
Defeat the Desert Snake
Defeat the Lord of the Winds
Defeat the Man-Eating Plant
Defeat the Ancient Demon
Defeat the Wyvern
Defeat the Wirewolf
Defeat the Unicorn
Make an Offering
Defeat the Iceshackle Cyclops
Defeat the Expert Thief
Survive an Explosion