Here is the full list of all 72 Artifacts of Eyru achievements.
Defeat the Pirate King as the Tinker
Defeat Sludge in the Pirate Sewers
Defeat Ratstalker in the Pirate Sewers
Unlocked your first Artifact from Toaster
Bought an upgrade or unlocked a weapon using Fae Moss
Bought an upgrade using Mist
Defeat Mycelius in the Fae Forest
Defeat the Pirate King as the Pirate
Defeat Captain Birdshot in the Pirate Sewers
Defeat the Rat King in the Pirate Sewers
Defeat Schrodinger in the Pirate Sewers
Defeat Lt. Muffins in the Pirate Sewers
Defeat the Pirate King as the Warlock
Defeat the Pirate King as the Wizard
Defeat the High Druid in the Fae Forest
Defeat the Sproutling Tender in the Fae Forest
Defeat the Bushmaster in the Fae Forest
Defeat the Grove Reaper in the Fae Forest
Defeat DJ Pop Rock in the Fae Forest
Defeat the Triumvirate of Tea as the Warlock
Defeat the Triumvirate of Tea as the Wizard
Defeat the Triumvirate of Tea as the Tinker
Defeat the Triumvirate of Tea as the Pirate
Defeat Rotmonger in the Lost Court
Defeat the Spirit Horde in the Lost Court
Defeat the Fallen Ranger in the Lost Court
Defeat Aed in the Lost Court
Defeat the Plunderer in the Lost Court
Defeat the Twin Colossi in the Lost Court
Defeat your Twisted Reflection as the Warlock
Defeat your Twisted Reflection as the Tinker
Defeat your Twisted Reflection as the Wizard
Defeat your Twisted Reflection as the Pirate
Defeat the Dagda as a Blood Warlock
Defeat the Dagda as a Spirit Warlock
Defeat the Dagda as a Void Warlock
Defeat the Dagda as a Sneaky Tinker
Defeat the Dagda as a Gadgeteering Tinker
Defeat the Dagda as a Grenading Tinker
Defeat the Dagda as a Plasma Wizard
Defeat the Dagda as an Astro Wizard
Defeat the Dagda as a Quantum Wizard
Defeat the Dagda as a Frenzy Pirate
Defeat the Dagda as a Tankin' Pirate
Defeat the Dagda as a Freebootin' Pirate
Defeat the Eternal Triumvirate as a Blood Warlock
Defeat the Eternal Triumvirate as a Spirit Warlock
Defeat the Eternal Triumvirate as a Void Warlock
Defeat the Eternal Triumvirate as a Sneaky Tinker
Defeat the Eternal Triumvirate as a Gadgeteering Tinker
Defeat the Eternal Triumvirate as a Grenading Tinker
Defeat the Eternal Triumvirate as a Plasma Wizard
Defeat the Eternal Triumvirate as an Astro Wizard
Defeat the Eternal Triumvirate as a Quantum Wizard
Defeat the Eternal Triumvirate as a Frenzy Pirate
Defeat the Eternal Triumvirate as a Tankin' Pirate
Defeat the Eternal Triumvirate as a Freebootin' Pirate
Defeat Nuada as a Blood Warlock
Defeat Nuada as a Spirit Warlock
Defeat Nuada as a Void Warlock
Defeat Nuada as a Sneaky Tinker
Defeat Nuada as a Gadgeteering Tinker
Defeat Nuada as a Grenading Tinker
Defeat Nuada as a Plasma Wizard
Defeat Nuada as an Astro Wizard
Defeat Nuada as a Quantum Wizard
Defeat Nuada as a Frenzy Pirate
Defeat Nuada as a Tankin' Pirate
Defeat Nuada as a Freebootin' Pirate
Unlocked all of the available Artifacts from Toaster
Bought all mist upgrades from Fig
Fully upgraded all starting weapons