Here is the full list of all 30 Hexelectric achievements.
Tutorial Stages Clear
Basic Rule Stages Clear
Probation Period Stages Clear
Novice Difficulty Clear
Zero Stages Clear
Anchor Stages Clear
Gear Stages Clear
Apprectice Difficulty Clear
Trigger Stages Clear
Revolver Stages Clear
Zodiac Stages Clear
Adept Difficulty Clear
Mechanic Stages Clear
Full House Stages Clear
Machine Gun Stages Clear
Expert Difficulty Clear
Master Difficulty Clear
All Stage Clear
All Stage Clear with full gauge
50 Rotations on a single stage
100 Rotations on a single stage
200 Rotations on a single stage
500 Rotations on a single stage
1000 Rotations on a single stage
Get 500 Battery Energy
Get 1000 Battery Energy
Get 2000 Battery Energy
Get 5000 Battery Energy
Get 10000 Battery Energy
Get 15000 Battery Energy