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