Learning the nuances of spelling and pronuncation rules will help emmensly.

Things like

И after Ж = Ы
Л before Ю = ЛЬ

This are things that no one will really tell you and things that native speakers also don't often think about or notice. They'll tell you that you still have an accent but won't be sure exactly how to correct it.

If you can remember these types of rules it will make your pronunciation a lot better.