Here is the full list of all 15 Breakout: Recharged achievements.
Destroy 7 blocks with a single bomb
Destroy 10 blocks with a single shot from a railgun
Have 3 balls on screen for 10 seconds
Destroy all blocks before the next collection of blocks shows up
Reach 2000 points in arcade mode
Reach 4000 points in arcade mode
Reach 6000 points in arcade mode
Survive for 300 seconds
Destroy 2000 blocks using explosive blocks
Bounce the ball 3 times without moving
Reach 500 points before the ball hits the platform
Complete all challenges in a single player mode
Destroy 4000 blocks using your bullets
Destroy 6000 blocks
Complete all challenges in coop mode