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