Here is the full list of all 23 Neon Invaders achievements.
Complete the EASY mode
Complete the NORMAL mode
Complete the HARD mode
Complete the EXTREME mode
Complete the CRAZY mode
Complete Level 10 on EASY mode
Complete Level 20 on EASY mode
Complete Level 30 on EASY mode
Complete Level 10 on NORMAL mode
Complete Level 20 on NORMAL mode
Complete Level 30 on NORMAL mode
Complete Level 10 on HARD mode
Complete Level 20 on HARD mode
Complete Level 30 on HARD mode
Complete Level 10 on EXTREME mode
Complete Level 20 on EXTREME mode
Complete Level 30 on EXTREME mode
Complete Level 10 on CRAZY mode
Complete Level 20 on CRAZY mode
Complete Level 30 on CRAZY mode