Why does Cosima Niehaus need glasses?

Directly from the show's Twitter page:

OBTrivia: Cosima wears glasses, her clones don't. Her sight degenerated due to her individual environment &conditions. She studies too hard!

So it seems a fun way to separate her from all the other clones. Nothing more unfortunately.

You make two assumptions one of which is wrong in science and the other of which is wrong even within the show universe.

Firstly, short sightedness is not primarily genetically determined. There may be some influence but rates of short sightedness in the real world depend strongly on the childhood environment. People who spend most of their time outdoors are far less likely to be short-sighted. The cliché is true: geeks who spend time with books are far more likely to be short-sighted. So Cosima, being a book geek, is the short sighted one.

The other assumption is that the clones are identical. Clearly this is not true even within the show universe. They clearly differ in mental and physical health: some are mentally unstable and some are physically ill (at least two have apparent respiratory problems by the end of series one, though one of those dies early of a gunshot wound, but she is ill before this). At least one of them is capable of having children but we know several others appear to be infertile. They are also not strictly genetically identical as their DNA is, at the very least, stamped with a unique ID. And there are hints that Dr Leekie is studying them partially to discover what those health problems are.

In short, there is no logical problem with the short-sightedness either inside or outside the show universe.