Here is the full list of all 22 NEO NEO achievements.
Reach the 4th zone.
Warp 40 times in a single run.
Get a score of 50
Reach the 3rd zone.
Reach the 2nd zone.
Get a score of 10
Reach the 5th zone.
Reach the 6th zone.
Get a score of 100
Get a score of 150
Get a score of 200
Warp 80 times in a single run.
With Infinite Warp, warp 80 times within 240 seconds.
With Shotgun Frenzy, kill 120 enemies within 180 seconds.
With Random Storm, kill 120 enemies within 180 seconds.
With Infinite Redz, kill 80 enemies within 120 seconds.
With Warp Blaster, reach 6th zone within 100 seconds.
With Speeed Runner, reach the 6th zone within 100 seconds.
Get a score of 300
Get a score of 400
Get a score of 500
With Iron Clad, kill 120 enemies within 180 seconds.