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