Here is the full list of all 59 Songs for a Hero - there are Definitive Edition achievements.
Find the last hidden useless spot.
Defeat The Seventh Boss While Taking No Damage
Defeat The Sixth Boss While Taking No Damage
Defeat The Sixth Secret Boss While Taking No Damage
Defeat The Fifth Boss While Taking No Damage
Defeat The Fith Secret Boss While Taking No Damage
Defeat The Fourth Boss While Taking No Damage
Defeat The Fourth Secret Boss While Taking No Damage
Defeat The Third Boss While Taking No Damage
Defeat The Third Secret Boss While Taking No Damage
Defeat The Second Secret Boss While Taking No Damage
Defeat The First Secret Boss While Taking No Damage
Mimic The Adventurer's Jump
Survive The Roling Stone.
Become The Super Hero
Use A Box To Slide On The Cliffs
Survive The Asteroids.
Defeat The Fourth Secret Boss
Defeat The Second Secret Boss
Find All Heart Container Pieces
Collect All Musical Notes
Find All Energy Container PIeces
Defeat The Sixth Secret Boss
Kill All Enemies During The Avalanche.
Open The Frozen Chest
Kill 20 Enemies During The Tornado.
Defeat The Fifth Secret Boss
Use The Minecart.
Solve The Pyramid Puzzle.
Defeat The Third Secret Boss
Defeat The First Secret Boss
Pet The Dog
Finish The Epilogue
Kill The Epilogue Sub Boss
Collect All HERO Letters
Finish The Eighth World
Kill 200 enemies
Kill 100 enemies
Collect 9999 Coins
Finish The First World
Finish The Second World
Finish The Third World
Finish The Fourth World
Finish The Fifth World
Finish The Sixth World
Finish The Seventh World
Defeat The Terrible Villain
Unlock the Flaming Sword
Unlock the Invisible Potion
Unlock the New Shield and Dive Skills
Unlock the Dash
Unlock the Double Jump
Unlock the Hookshot
Unlock the Crossbowmerang
Learn All Sword Moves
Collect Half Musical Notes
Grab All The Minecart Coins
Defeat The Second Boss While Taking No Damage
Defeat The First Boss While Taking No Damage