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.
Obtain all head gear
Obtain all arm gear
Complete the guide
Visit all locations on Flammie
Reach the ending
Defeat Mana Beast
All weapons at level 9
Defeat all monsters
Defeat Dark Lich
All magic at level 8
Obtain all torso gear
Defeat Dread Slime
Defeat King Vampire
Defeat Blue Dragon
Defeat Kettle Kin
Defeat Mech Rider 3
Defeat Aegagropilon
Defeat Shadows #1, 2 & 3
Defeat Gorgon Bull
Defeat Dark Stalker
Defeat Mech Rider 2
Defeat Lime Slime
Defeat Vampire
Defeat Frost Gigas
Defeat Minotaur
Defeat Boreal Face
Defeat Great Viper
Defeat Mech Rider
Defeat Spring Beak
Defeat Kilroy
Defeat Jabberwocky
Defeat Wall Face
Defeat Fire Gigas
Defeat Biting Lizard
Defeat Spikey Tiger
Defeat Tropicallo
Defeat Mantis Ant