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