Here is the full list of all 21 BIT.TRIP CORE achievements.
Blast all Beats during a Challenge
Beat Discovery in Normal difficulty
Beat any level without using a Bomb in Normal difficulty
Chained 100 Beats
Register a high score on the leaderboards
Escaped Nether Mode
Get a PERFECT score in Discovery
Get a PERFECT score in Exploration
Get a PERFECT score in Control
Achieved a multiplier of 50 in Normal difficulty
Achieved a multiplier of 100 in Normal difficulty
Chained 200 Beats
Play through one entire stage in Super Mode in Normal difficulty
Chained 500 Beats
Watched the hidden cutscene
Beat Exploration in Normal difficulty
Beat Control in Normal difficulty
Beat the game in one sitting without getting a Game Over
Blast 10,000 Beats
Blast 30+ Beats at once with one Bomb
Beat the game on Normal difficulty