Here is the full list of all 23 Eldritch Hunter achievements.
Complete Stage 1.
Complete Stage 2.
Complete Stage 3.
Beat Stage 3 Level 1 in under 8 seconds.
Complete Stage 4.
Complete Stage 5.
Beat Stage 1 Level 2 in under 12 seconds.
Beat Stage 1 Level 5 in under 8 seconds.
Beat Stage 1 Level 3 in under 10 seconds.
Beat Dagon with the Broadsword. Must be the only weapon used during the fight.
Beat Stage 2 Level 6 in under 10 seconds.
Beat Stage 3 Level 6 in under 15 seconds.
Beat Stage 3 Level 4 in under 15 seconds.
Beat Stage 4 Level 2 in under 11 seconds.
Beat Stage 4 Level 4 in under 17 seconds.
Beat Stage 4 Level 6 in under 10 seconds.
Beat Stage 5 Level 2 in under 10 seconds.
Beat Stage 5 Level 4 with the Bubble Gun. Must be the only weapon used during the level.
Beat Stage 6 Level 3 in under 10 seconds.
Beat Stage 6 Level 2 in under 16 seconds.
Complete Stage 6.
Beat Stage 1 Level 4 in under 12 seconds.
Beat Stage 1 Level 7 in under 7 seconds.