Here is the full list of all 51 OKAMI HD achievements. It takes around 40-50 hours to unlock all of the achievements on Windows.
Defeat Orochi.
Learn how to use Inferno.
Enter the Moon Cave.
Defeat the Crimson Helm.
Learn how to use Galestorm.
Learn how to use Crescent.
Learn how to use Watersprout.
Beat Hayabusa's turnip-digging record.
Defeat the imps that possessed Princess Fuse.
Exterminate the Spider Queen.
Learn how to use Vine.
Fight Waka.
Learn how to use Water Lily.
Learn how to use Cherry Bomb.
Defeat enemies inside of a Devil Gate.
Learn how to use Bloom.
Meet Susano.
Return Kamiki Village back to normal.
Earn a Cherry Tree rank for each item in the Results screen.
Learn how to use Power Slash.
Learn how to use Rejuvenation.
Make your way to shore without being swallowed by the Water Dragon.
Learn how to use Veil of Mist.
Defeat Blight.
Learn how to use Catwalk.
Meet Otohime.
Defeat Evil Rao.
Learn how to use Thunderstorm.
Win the final race against Tobi.
Defeat Ninetails.
Defeat True Orochi.
Learn how to use Blizzard.
Defeat the twin demons, Lechku and Nechku.
Board the Ark of Yamato.
Defeat Yami.
Increase your Solar Energy, Ink Pot, and Astral Pouch levels to maximum capacity.
Complete your Fish Tome.
Complete your Travel Guide.
Complete your Treasure Tome.
Defeat all monsters on the Wanted List.
Collect all Stray Beads.
Complete your Animal Tome.
Learn all god techniques to fill up your Technique Scroll.
Complete your Bestiary.
Earn a Cherry Tree rank for each item in the Total Results screen.
Defeat all enemies at all three Devil Gate trial caves.
Defeat the Kusa 5.
Complete five digging mini games.
Win the race against Ida and Hayate.
Win the race against Kai.
Unlock all achievements.