Here is the full list of all 51 Pyre trophies - there are 38 bronze, 10 silver, 2 gold and 1 platinum.
Complete a Rite against another mortal (Versus Mode)
Complete your quest for freedom (Campaign)
Use Scribe Snuff to reset an exile's Masteries (Campaign)
Prevail in a Rite in no more than three dousings (Campaign)
Prevail in a Rite with 12 Titan Stars active (Campaign, standard difficulty or greater)
Prevail in a Rite with six or more Titan Stars active (Campaign, standard difficulty or greater)
Prevail in a Rite with three or more Titan Stars active (Campaign, standard difficulty or greater)
Using the Stowaway, deal 200 Pyre Damage (Campaign)
Suffer defeat in a Liberation Rite (Campaign)
Complete three Feats of Glory (Campaign)
Spend 1,000 Sol in the Slugmarket (Campaign)
Using Sir Gilman, deal 200 Pyre Damage (Campaign)
Using Bertrude, deal 200 Pyre Damage (Campaign)
Do Vocations 10 times (Campaign)
Unlock every chapter in the Book of Rites (Campaign)
While flying, bump into five different adversaries' wagons (Campaign)
While flying, interact with 10 different observation points (Campaign)
Find an exile for each of the different masks (Campaign)
Liberate any three exiles from your party (Campaign)
Check 50 different pages in the Book of Rites (Campaign)
Prevail in a Rite against each of the other triumvirates (Campaign)
Achieve Rank 5 with any exile (Campaign)
Prevail in a Rite at each of the Celestial Landmarks (Campaign)
Upgrade a Talisman to Rank 20 (Campaign)
Complete five Scribe Trials in the Beyonder Crystal (Campaign)
Complete a Practice Rite in the Beyonder Crystal (Campaign)
Using Pamitha, deal 200 Pyre Damage (Campaign)
Initiate 20 different conversations in the blackwagon (Campaign)
Prevail in a Rite using Jodariel and Pamitha (Campaign)
Using Jodariel, deal 200 Pyre Damage (Campaign)
Prevail using Volfred, Ti'zo, and Oralech (Versus Mode)
Prevail using Rukey, Barker, and Dalbert (Versus Mode)
Prevail at the Isle of Khaylmer using Ti'zo and Messenger Imp (Versus Mode)
Prevail using Sandra, Tamitha, and Udmildhe (Versus Mode)
Using Ti'zo, deal 200 Pyre Damage (Campaign)
Prevail in a Liberation Rite (Campaign)
Using Hedwyn, deal 200 Pyre Damage (Campaign)
Use the White Lute to play a tune (Campaign)
Complete a Rite against a CPU opponent (Versus Mode)
Complete two Scribe Trials in the Beyonder Crystal (Campaign)
Using Rukey, deal 200 Pyre Damage (Campaign)
Prevail in a Rite without your Pyre taking damage (Campaign)
During a Rite, fling the Orb at an adversary, then banish them within two sec. (Campaign)
Begin your quest for freedom (Campaign)
Earn all other available trophies in Pyre.
Using Volfred, deal 200 Pyre Damage (Campaign)
Prevail in a Rite against a CPU opponent while you have less than 10 Pyre Health (Versus Mode with default Masteries, Talismans, Pyre Health)
Prevail in a Rite against a Master-level CPU opponent (Versus Mode, default Talismans and Masteries)
During a Rite, banish three adversaries with a single Aura Cast (Campaign)
During a Rite, douse the adversary's Pyre by 40 health or more (Campaign)
Prevail against a Master CPU opponent with six or more Titan Stars active (Versus Mode with default Masteries, Talismans, Pyre Health)