Here is the full list of all 27 Eldritch Exterminators achievements.
Play a single run
Kill 7200 Enemies
Achieve a Critical Chance of 40%
Obtain 760 RPM Fire Rate in a Single Run
Beat 3 Runs
Survive for 5 minutes
Obtain a projectile count of 5 in Single Run
Stand Still for 1 Minute
Spend 2 minutes under 50% health
Beat Darkness Encroaches with Cathilan's Repeater
Kill 2000 enemies
Have 3 Curses
Win a Run with less than 3 Health
Beat Darkness Encroaches with Dretch Bane
Kill 20 Bosses
Beat Darkness Encroaches with Goruk's Doorbell
Beat Darkness Encroaches with Harrath's Peace
Beat Darkness Encroaches with Madruger
Spend 2 minutes without shooting
Beat Darkness Encroaches with Shrike
Obtain 200 Trinkets
Win a single round
Beat Darkness Encroaches with Adiras's Wrath
Kill 1000 Enemies with blast damage
Beat Darkness Encroaches with Borillis Blaster
Achieve a Critical Chance of 100%
Have 10 Dash Charges