Here is the full list of all 52 Elements: Soul of Fire achievements.
Recover Ben's undead statue.
Obtain the secret ending.
Defeat the final boss in ten turns or less.
Defeat the final boss with Leonardo alone.
Clear the game in under 40 hours.
Defeat Saruma.
Defeat the Iron Emperor.
Defeat Dark Saint.
Learn Flame Meteor.
Learn Astral Fire.
Learn Flare Dazzle.
Recover Ben's insect statue.
Recover Ben's avian statue.
Recover Ben's machine statue.
Recover Ben's beast statue.
Recover Ben's plant statue.
Recover Ben's aquan statue.
Recover Ben's demon statue.
Recover Ben's morph statue.
Recover Ben's reptile statue.
Recover Ben's humanoid statue.
Return all of Ben's statues.
Receive Priestess Anya's blessing.
Receive Priestess Lola's blessing.
Receive Priestess Nora's blessing.
Receive Priestess Yuri's blessing.
Receive Priestess Cynthia's blessing.
Receive Priestess Gilda's blessing.
Receive Priestess Mona's blessing.
Receive Priestess Vivi's blessing.
Receive Priestess Yoko's blessing.
Receive Priestess Jordine's blessing.
Receive Priestess Ella's blessing.
Receive Priestess Vanessa's blessing.
Cure Pica's curse.
Give Dimitri all eight kinds of shards, crystals, or rings.
Bring Ms. Pearl at least five pearls in total.
Obtain Excalibur.
Bring all three Relics of the Zodiac to ???.
Recruit ???.
Complete the Arean-Alavon Cross-Country Race.
Administer the Panacea Root to Granny.
Complete the switch track in Glymac Mines.
Complete the jump track in Glymac Mines.
Obtain the Phoenix Claws.
Obtain the Raft.
Meet Great-Granny.
Save all of Cinnamon's pets.
Catch the thief in Ikory.
Pass the exam at Reikya Academy.
Obtain the Sigil of Immanuel.
Win 100 consecutive battles in the Arena Challenge.