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