Here is the full list of all 56 Mysterious Realms RPG achievements.
Slay Elemental Lord
Drink 40 potions
Slay Grim Reaper
Encounter 5 strangers
Slay Goblin King
Complete 20 missions
Empower every Crystal up to 5 power
Encounter 3 strangers
Drink 15 potions
Slay 10 rare enemies
Solve 8 riddles
Light 100 torches
Teach every Hero 6 skills
Drink 5 potions
Eat 10 food
Examine 15 objects
Encounter 25 Events
Slay 5 rare enemies
Slay 100 enemies
Unlock every feature in the Town
Open 100 vases, barrels etc.
Complete 10 missions
Eat 3 food
Light 50 torches
Empower every Crystal up to 3 power
Examine 8 objects
Pick up 100 salvage
Encounter a stranger
Pick up 200 gold
Open 50 vases, barrels etc.
Encounter 10 Events
Pick up 40 salvage
Pick up 100 gold
Examine 3 objects
Slay 25 enemies
Solve 3 riddles
Teach every Hero 4 skills
Pick up 30 gold
Pick up 10 salvage
Slay 10 enemies
Slay a rare enemy
Open 10 vases, barrels etc.
Light 5 torches
Solve a riddle
Teach Hero a skill
Empower a Crystal up to 3 power
Complete a mission
Encounter an Event
Slay the first enemy
Complete a mission when one Hero is dead
Reach the maximum of enemy's Health modif.
Slay the First Warden
Slay a hidden enemy
Eat 25 food
Complete the game without any Hero dying
Obtain every other achievement