Here is the full list of all 33 Imperatum achievements.
Kill Worm
Kill Urxxus
Kill Urxxus 2.0
Kill a champion monster
Equip a rare item
Equip a set item
Equip a unique item
Equip a new stim
Use a currency item
Equip an uncommon or better item in every slot
Equip a rare or better item in every slot
Equip a unique item in every slot
Upgrade an item to uncommon
Upgrade an item to rare
Upgrade an item to set
Upgrade an item to unique
Reroll the affixes on a rare item
Reroll the affixes on a unique item
Reroll the affixes on a set item
Mirror an item
Purchase a skill
Purchase a skill from every class
Level a skill up to 5
Socket a skill in passive mode
Complete Mission 1
Complete Mission 2
Complete Mission 3
Complete Mission 4
Complete Mission 5
Complete Mission 6
Complete Mission 7
Complete Mission 8
Kill Tucoz