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