Adding support for Unicode passwords it an important feature that should not be ignored by developers.
Still, adding support for Unicode in passwords is a tricky job because the same text can be encoded in different ways in Unicode and you don't want to prevent people from logging in because of this.
Let's say that you'll store the passwords as UTF-8, and mind that this question is not related to Unicode encodings and it's related to Unicode normalization.
Now the question is how you should normalize the Unicode data?
You have to be sure that you'll be able to compare it. You need to be sure that when the next Unicode standard will be released it will not invalidate your password verification.
Note: still there are some places where Unicode passwords will probably never be used, but this question is not about why or when to use Unicode passwords, it is about how to implement them in the proper way.
1st update
Is it possible to implement this without using ICU, like using OS for normalizing?