Here is the full list of all 51 Pyre achievements. It takes around 20-25 hours to unlock all of the achievements on Windows.
Using Volfred, deal 200 Pyre Damage (Campaign)
Prevail using Rukey, Barker, and Dalbert (Versus Mode)
Prevail using Volfred, Ti'zo, and Oralech (Versus Mode)
Prevail at the Isle of Khaylmer using Ti'zo and Messenger Imp (Versus Mode)
Unlock every chapter in the Book of Rites (Campaign)
Prevail in a Rite against a Master-level CPU opponent (Versus Mode, default Talismans and Masteries)
Prevail against a Master CPU opponent with six or more Titan Stars active (Versus Mode with default Masteries, Talismans, Pyre Health)
Complete a Rite against a CPU opponent (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)
Complete your quest for freedom (Campaign)
Spend 1,000 Sol in the Slugmarket (Campaign)
Prevail in a Rite with 12 Titan Stars active (Campaign)
Prevail in a Rite with six or more Titan Stars active (Campaign)
Use Scribe Snuff to reset an exile's Masteries (Campaign)
Achieve Rank 5 with any exile (Campaign)
Prevail in a Rite with three or more Titan Stars active (Campaign)
Complete three Feats of Glory (Campaign)
Find an exile for each of the different masks (Campaign)
Check 50 different pages in the Book of Rites (Campaign)
Liberate any three exiles from your party (Campaign)
Prevail in a Rite in no more than three dousings (Campaign)
Using Bertrude, deal 200 Pyre Damage (Campaign)
During a Rite, douse the adversary's Pyre by 40 health or more (Campaign)
While flying, interact with 10 different observation points (Campaign)
Prevail in a Rite against each of the other triumvirates (Campaign)
Using Sir Gilman, deal 200 Pyre Damage (Campaign)
Using Pamitha, deal 200 Pyre Damage (Campaign)
Prevail in a Rite at each of the Celestial Landmarks (Campaign)
Do Vocations 10 times (Campaign)
Complete a Practice Rite in the Beyonder Crystal (Campaign)
Prevail in a Rite using Jodariel and Pamitha (Campaign)
Using Jodariel, deal 200 Pyre Damage (Campaign)
Prevail in a Rite without your Pyre taking damage (Campaign)
Using Ti'zo, deal 200 Pyre Damage (Campaign)
Complete five Scribe Trials in the Beyonder Crystal (Campaign)
While flying, bump into five different adversaries' wagons (Campaign)
Using Hedwyn, deal 200 Pyre Damage (Campaign)
Initiate 20 different conversations in the blackgwagon (Campaign)
Prevail in a Liberation Rite (Campaign)
Using the Stowaway, deal 200 Pyre Damage (Campaign)
Upgrade a Talisman to Rank 20 (Campaign)
Complete two Scribe Trials in the Beyonder Crystal (Campaign)
During a Rite, banish three adversaries with a single Aura Cast (Campaign)
Use the White Lute to play a tune (Campaign)
Using Rukey, deal 200 Pyre Damage (Campaign)
During a Rite, fling the Orb at an adversary, then banish them within two sec. (Campaign)
Begin your quest for freedom (Campaign)
Suffer defeat in a Liberation Rite (Campaign)
Complete a Rite against another mortal (Versus Mode)
Prevail using Sandra, Tamitha, and Udmildhe (Versus Mode)
Complete your quest for freedom (Campaign, True Nightwing difficulty)