Here is the full list of all 45 Beat Hazard 3 achievements.
Blast 100,000 Kilotons of Bosses
Successfully Complete 5 Tracks
Level Up to Officer 3rd Class
Level Up
Successfully Complete a Track
Take Out a 10,000 Kiloton Boss
Take Out a 5,000 Kiloton Boss
Take Out a 500 Kiloton Boss
Successfully Complete 20 Tracks
Successfully Complete 50 Tracks
Successfully Complete 75 Tracks
Successfully Complete 100 Tracks
Level Up to Captain
Level Up to Elite Rank
Play for 1 (non Steam) Hour
Play for 2 (non Steam) Hours
Play for 3 (non Steam) Hours
Play for 4 (non Steam) Hours
Play for 5 (non Steam) Hours
Reach Wave 10 in Boss Rush
Reach Wave 20 in Boss Rush
Reach Wave 30 in Boss Rush
Take Out a 15,000 Kiloton Boss
Blast 200,000 Kilotons of Bosses
Blast 500,000 Kilotons of Bosses
Blast 1,000,000 Kilotons of Bosses
Complete a 4+ minute track on 500% difficulty or higher
Complete a 4+ minute track on 600% difficulty or higher
Complete a 4+ minute track on 700% difficulty or higher
Complete a 4+ minute track on 800% difficulty or higher
Score over 1,000,000 playing the Beat Hazard 3 theme
Score over 1,000,000 playing Beginning Trancemission
Score over 1,000,000 playing Biohacker
Score over 1,000,000 playing Edge Of Space
Score over 1,000,000 playing Fractal Diver
Score over 1,000,000 playing Lethal Trip
Score over 1,000,000 playing Life Line
Score over 1,000,000 playing Ouverture
Score over 1,000,000 playing Shock Wave
Score over 1,000,000 playing Stadium Wave
Score over 1,000,000 playing Transmutation
Come 1st, 2nd or 3rd in a daily/lightning challenge
Place top 10 in a daily/lightning challenge
Place top 10 in a daily/lightning challenge 5 times
Place top 10 in a daily/lightning challenge 10 times