Here is the full list of all 28 Harvest Moon: Light of Hope achievements.
Make strawberry jam and revive the Harvest Goddess.
Place four stone tablets by the lighthouse.
Become friends with someone.
Place three stone tablets by the lighthouse.
Learn the basics of farming.
Place the first stone tablet by the lighthouse.
Get an axe to cut down trees.
Get a fishing rod to catch fish.
Place two stone tablets by the lighthouse.
Get a hammer to break rocks and mine ore.
Unlock all achievements.
Catch all fish.
Harvest all crops.
Harvest all flowers.
Mine all gems and ore.
Cook all recipes.
Record all items in the encyclopedia.
Win the Cooking Festival, Fishing Festival, and Dog Race on Advanced.
Reach the bottom of the mine.
Place the last stone tablet by the lighthouse and revive the island.
Become closer to a friend.
Become a good friend with someone.
Become more than friends with someone.
Propose marriage to someone.
Get married to someone.
Have a child.
Using medicine, cure your child from Petrifaction.
Have your child grow up.