Here is the full list of all 29 NEOMORPH achievements.
Stage 1 Clear
Defeat Boss
Kill 1500 Enemies
Kill 2000 Enemies
Kill 2500 Enemies
Kill 3000 Enemies
Kill 4000 Enemies
Kill 9000 Enemies
Kill 15000 Enemies
Kill 6000 Enemies
Kill 1000 Enemies
Date With Girl NO.4 2 Times
Date With Girl NO.4 1 Time
Date With Girl NO.3 2 Times
Date With Girl NO.3 1 Time
Stage 8 Clear
Stage 7 Clear
Stage 6 Clear
Stage 5 Clear
Date With Girl NO.2 2 Times
Date With Girl NO.2 1 Time
Stage 4 Clear
Stage 3 Clear
Date With Girl NO.1 2 Times
Stage 2 Clear
Kill 600 Enemies
Kill 300 Enemies
Kill 100 Enemies
Date With Girl NO.1 1 Time