First thing could be how many balloons were shot down, so something like
percentage_hit = hits/total_number_of_balloons
Afterwards, you can factor in accuracy, with
accuracy = hits/total_shots
So a basic scoring would be accuracy*percentage_hit
. You might want to add a *100
or so in there, so the score is a bigger number.
Another idea would be to assign every balloon hit a score, maybe based on how long it is on the field already. So if the players hits it very fast after it appears, it is worth more than when it is on the field longer.