Here is the full list of all 26 Inkulinati achievements.
Turn a friendly Beast into a Heretic.
Win a battle in Journey Mode without taking any Damage to your Tiny Inkulinati.
Defeat Godfrey.
Win an Elite Battle during your Journey.
Collect five different Beast races in one run.
Defeat the Master.
Win the first battle during your Journey.
One-shot a Beast.
Kill an enemy with a friendly Beast that has 1 Health remaining.
Kill a Heretic with a Bishop.
Complete the Tutorial.
Kill an enemy that killed a friendly Beast.
Complete last Advanced Lesson.
Win every Advanced Lesson.
Defeat the Master after the Resoiréection.
Defeat Hildegard.
Defeat Dante.
Defeat Death on Easy or Normal Mode.
Defeat Death on Hard Mode.
Win a battle without any Beasts at the end during Journey Mode.
Win a battle in Journey Mode while your Tiny Inkulinati has just 1 Health remaining.
Collect a total of 5000 Prestige points.
Defeat Death on Master Mode.
Defeat Ape Profesor.
Defeat Francis.
Win the last battle in Act VII.