Here is the full list of all 23 Super Laser Racer achievements.
Destroy an opponent with a Laser
Destroy an opponent with the Super Laser
Use tractor beam to overtake opponent
Destroy an opponent with a Plasma
Destroy multiple enemies in a race
Destroy an opponent with Mines
Destroy a Bomb before it explodes
Win a race without using a weapon
Complete a lap without taking any damage
Win a race
Win a Survivor quick race
Win an Eliminator quick race
Unlock all ships
Earn a Special medal
Unlock all tournaments (Hard)
Destroy an opponent with the Cannon
Destroy an opponent with a Missile
Destroy an opponent with a Bomb
Use Shield to protect yourself from a Missile
Destroy an enemy in your death blast
Special medal for Super tournament (Hard)
Earn all the Special medals on all levels
Destroy mine with an ECM blast