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