Here is the full list of all 18 Empyrean Swarm achievements.
Completed chapter one.
Completed chapter two.
Completed chapter three.
Completed chapter four.
Once you've already seen his cutscene once, keep the introductory squid alive for the entire first level.
Completed chapter five.
Unlocked the Shield System.
Unlock the Alert System.
Unlock the Upgraded Alert System.
Unlocked the Booster System
Beat the story without gaining a single level through the Adaption system.
Unlocked The Void.
Started a run in The Void
Reach Level 42 with the Daddy.
Die at least 100 times on one save file.
On a fresh file, kill Mr Squid for the first time without taking damage.
Discover the looming threat in the Void.
Beat the story without a single death on a fresh file.