Here is the full list of all 30 Mystery Chronicle: One Way Heroics achievements.
Clear any world other than the tutorial on Easy.
Take 3 Allies with you on your adventure.
Expand the castle.
Win an online match.
Battle another hero in an online match for the first time.
Gain ability to customize the castle.
Acquire all trophies.
Clear a world on Normal.
Clear a world on Hard.
Clear a world on Very Hard.
Defeat Fallen Angel Alma on Normal or higher difficulty.
Defeat Zeukrees, the Giant of Light.
Defeat Pluton.
Reach the End of the East.
Reach the End of Dreams.
Reach the end of the world.
Recruit all residents.
Complete a quest that unlocks a class.
Unlock all classes.
Clear on Normal or higher difficulty with all classes.
Open 50 treasure chests on 1 adventure.
Open 100 treasure chests on 1 adventure.
Defeat 100 monsters on 1 adventure.
Defeat 200 monsters on 1 adventure.
Expand Dream Vault to maximum size.
Defeat the Bug Emperor.
Battle in 10 online matches.
Win 10 online matches in a row.
Obtain an extra medal.
Unlock all epilogues.