Here is the full list of all 67 PERISH achievements.
The base game contains 63 achievements, and there is 1 DLC pack containing 4 achievements.
Perish in the Ruins of Tartaros
Reach Tartaros
Kill 500 Athanatoi
Survive Charon's Isle
Survive Charon's Trireme
Defeat the Karkinos
Survive the Maelstrom of Charybdis
Survive the Run through the Maelstrom of Charybdis
Survive the Thalassian Fissure
Escort the Procession and Complete the Ritual
Bank 1000 Danake
Defeat Kakos the Fire Sentinel
Survive the Foundry of Hephaestus
Reconstruct and Reanimate Talos
Survive the Arena in The Trajan Palace
Rebuild the Shattered Bridge
Survive the Trajan Palace
Drain the Sewer in the Trajan Palace
Defeat Deimos and Phobos
Survive Ophion's Labyrinth
Kill 50 Ophidians
Defeat Python
Rebuild and Fire the Ballista
Rebuild and Survive the Lodestone
Defeat the Kathorao
Survive the Euxine Gorge
Charge the Sarcophagus
Raze the Temple to the Ground
Release the Tormented from Their Cages
Purchase Your First Weapon
Survive the Orphic Temple Arena
Survive the Temple of the Nekromanteion
Kick 1 Athanatos off a Ledge
Slay the Minotauroi
Light the Four Braziers in the Orphic Temple
Fail a Journey to Elysium
Survive the Orphic Temple
Kick 1 Athanatos and Dispatch with a Headshot
Defeat the Orphic Champion
Kill 1 Athanatos with a Dagger
Ransack the the Trajan Palace
Work the Crucible and Place the Statue
Recover the Pearls and Raise the Statue
Complete the Apollo Rite
Complete the Dionysus Rite
Complete the Persephone Rite
Kill 1000 Athanatoi
Kill 100 Kourai
Kill 50 Cyclopes
Kill 50 Fury
Defeat the Kathorao 10 Times
Kill 100 Kavouraki
Bank 5000 Danake
Bank 10,000 Danake
Bank 50,000 Danake
Bank 100,000 Danake
Detonate with the Detonation Crown
Reach Elysium
Unlock All Items
Purchase Every Item in the Shop
Find all the Orphic Fragments
Complete the Codex
Earn your Place in the Elysian Fields
Act I: Liberated the prisoners in the Zephyrean realm
Act II: Thawed and defeated the frozen nemesis Aquilo
Act III: Escaped the vast jaws of the Skolex
Act IV: Defeated Vulturus with the Aegis shield