Here is the full list of all 37 Secret of Mana achievements. It takes around 25-30 hours to unlock all of the achievements on Windows.
Defeat Jabberwocky
Defeat Kilroy
Defeat Wall Face
Defeat Fire Gigas
Defeat Biting Lizard
Defeat Spikey Tiger
Defeat Tropicallo
Defeat Mantis Ant
Defeat Spring Beak
Defeat Great Viper
Defeat Boreal Face
Defeat Frost Gigas
Defeat Mech Rider
Defeat Minotaur
Defeat Vampire
Defeat Mech Rider 2
Defeat Lime Slime
Defeat Gorgon Bull
Defeat Dark Stalker
Defeat Shadows #1, 2 & 3
Defeat Aegagropilon
Defeat Kettle Kin
Defeat Mech Rider 3
Defeat Blue Dragon
Defeat Mana Beast
Reach the ending
All weapons at level 9
All magic at level 8
Visit all locations on Flammie
Complete the guide
Defeat all monsters
Obtain all torso gear
Obtain all head gear
Obtain all arm gear
Defeat King Vampire
Defeat Dread Slime
Defeat Dark Lich