Here is the full list of all 15 Neon Aileron achievements.
Beat the first level
Start a game on hard difficulty
Play Neon Aileron 2 days in a row
Start a game before 8am.
Beat Neon Aileron on Hard difficulty.
Continue 3 times in Neon Aileron
Use a continue
Collect all of the greenscreen achievements
Clear the game without continuing
Beat the game as Duane Jersone
Beat the game as Dwight Speed
Beat the game as Jane Reaction
Beat a level without taking any damage
Destroy all targets in a level
Reach the true last level