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