The problem is that you are giving "good score" the zero article. This transforms the noun phrase from its intended meaning into either a proper noun (the name of something) or a mass noun (which is nonsense).
With the zero article, your sentence is basically saying that there is a person or physical object (like a book or something) with the name "good score", and that you want to "get" this thing. This is clearly not your intended message, and so it is grammatically wrong.
Plural nouns get the zero article by default, just as mass nouns do, which is why "If you want to get good scores" is correct.
An example of the proper use of the zero article would be in something like the word "Rose". With the indefinite or definite article (a, the) it means a flower. With the zero article instead, it is a common girl's name. As the article I linked above gives in example:
My mother's name is Rose. I gave her a rose on Mother's Day.
If I changed this to say:
I gave her Rose on Mother's Day.
It now means that I have given my mother a girl named Rose, which depending on context, could either mean something like "giving her a granddaughter named Rose" or "giving her a chattel slave named Rose".