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