You need to listen to a lot of native speakers to adapt their accent. But then again which accent do you want to adapt? British? American? Australian?
Further, those accents break down into a lot of sub-accents based on the geographical location of the country. But with enough practice you can reach a level where native speakers would not hear the subtle differences in your pronunciation and you'll be speaking just like any native speaker in that area.
I think it's impossible to really speak as a native speaker. You'll always have to improve in some ways that you cannot see before reaching a close-to-bilingual level.
You can just improve. The only questions are: what's your current level ? what are the points you're not satified with ? what's your goal by speaking "like a native speaker" ?