For this achievement, you need to complete the first stage. This stage has you against bi-planes that shoot bullets and drop bombs (which you can shoot down to unlock “Missile Attack 1”). There is a meter along the bottom of the screen to track your progress on how many enemies you’ve killed, which reduces as you shoot them down. Once you’ve killed 56 enemy bi-planes, a blimp will appear. Destroy it (it takes 7 hits) to unlock this achievement.
You can lose lives and still obtain this achievement as long as you complete the stage.