Here is the full list of all 20 Emorrior achievements.
Kill 1 enemy
Kill 50 enemy
Have 1000 spirits in one run.
Kill the first boss.
Earn 10000 spirits in one run.
Have 10000 spirits in one run.
Enter the 19th room
Kill the second boss.
Enter the 29th room
Kill the third boss.
Earn 1000000 spirits in one run.
Enter the 39th room
Kill the 4th boss
Kill the 5th boss
Kill the first boss with second difficult
Kill the third boss with third difficult
Kill the 5th boss with 5th difficult
Have 999999999 spirits in one run.