Here is the full list of all 31 MIGHTY GUNVOLT BURST achievements.
Clear the stage under certain conditions
Clear the game as Ekoro
Clear the game as Gunvolt
Clear the game in under 1 hour
Clear all stages using Custom Slot No. 1
Clear a stage without taking any damage
Clear a stage without using any Bursts
Beat all bosses using their weaknesses
Clear the game as Beck
Defeat all 8 of the Mighty Numbers
Clear a stage with 1500+ CP of equipment
Clear a stage with an 'S' rank
Clear the opening stage
Defeat a boss using Burst
Get a Burst Combo of 10+ & clear a stage