Here is the full list of all 28 Harvest Moon: Light of Hope achievements.
Become more than friends with 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 a good friend with someone.
Become closer to a friend.
Make strawberry jam and revive the Harvest Goddess.
Place four stone tablets by the lighthouse.
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.
Learn the basics of farming.
Place the first stone tablet by the lighthouse.
Get an axe to cut down trees.
Place two stone tablets by the lighthouse.
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.