Here is the full list of all 28 Harvest Moon: Light of Hope achievements.
Mine all gems and ore.
Reach the bottom of the mine.
Become more than friends with someone.
Become a good friend with someone.
Place the last stone tablet by the lighthouse and revive the island.
Make strawberry jam and revive the Harvest Goddess.
Place four stone tablets by the lighthouse.
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.
Propose marriage to someone.
Get married to someone.
Have a child.
Using medicine, cure your child from Petrifaction.
Have your child grow up.