[Vibovit]

Honestly, I don't believe you can ever get rid of your native accent.
And I also underestimated that problem until my first contacts with "real" English, I mean communication with people whose mother tongue it was.
One's pronounciation difficulties probably vary depending on where they are from - the set of sounds that your first language consists of, determines which bits of English will be difficult to you.
Personally I think that intonation is very important, too - another thing which I underestimated in the past - it plays a great role in getting accross, and fortunately, it's much easier to be improved (in my opinion).