Here is the full list of all 28 Harvest Moon: One World achievements.
Unlock all achievements.
Catch every type of fish.
Harvest every type of crop.
Harvest every type of flower.
Mine every type of gem and ore.
Cook every type of dish.
Win in Advanced level in every contest, such as the Red Hot Cook-Off and Equestrian Challenge.
Harvest the first crop you grew yourself.
Set up your farm for the first time.
Chop down a tree for the first time.
Mine ore for the first time.
Catch a fish for the first time.
Get the Medallion near your home.
Get the Medallion in Calisson.
Get the Medallion in Halo Halo
Get the Medallion in Pastilla.
Get the Medallion in Lebkuchen.
Get the Medallion in Salmiakki.
Become friends with someone.
Become better friends.
Become friends on a deeper level.
Become more than friends.
Have a wedding.
Have a child.
Find your missing child.
Your child grows up.
Harvest 100 high-quality crops and flowers.
Give lots of gifts to the townspeople.