Here is the full list of all 38 Hero of the Kingdom achievements. It takes around 4-5 hours to unlock all of the achievements on Windows.
Find 300 mushrooms.
Find 60 lost crates and barrels.
Find 140 eggs.
Destroy the Dark Lord.
Find 12 pearls.
Fight 12 battles.
Make 25 sun solutions.
Have 350 fame.
Catch 160 fish.
Find 12 treasures.
Heal five people.
Hunt down 65 wild animals.
Help two ghosts.
Find father.
Build or repair 10 structures.
Rest 50 times in a camp.
Gather 15 barrels of algae.
Learn an expert skill.
Find 25 crayfish.
Pick 45 herbs.
Gather 40 sacks of night flowers.
Find 30 lost crates and barrels.
Find 150 mushrooms.
Catch 80 fish.
Hunt down 25 wild animals.
Become a soldier.
Have 100 fame.
Learn an advanced skill.
Get a boat.
Own 5,000 gold coins.
Own 500 gold coins.
Finish the water mill.
Learn three skills.
Get a weapon.
Make a barter.
Leave the home farm.
Saw 10 pieces of wood.
Get working tools.