For everybody who answered that it is possible I wonder if they have actually done it. If not then I have news for you. I have never met a person who has achieved it after the age of 18 including myself.
Spent a lot of time on languages in my life, being fluent in four of them, but speak with no accent only in my native language.
Took courses in pronunciation, private lessons in pronunciation, courses in other aspects of the language. Definitely improved a lot, but the issue with accent is that people react to it in a binary form. It does not matter how good you are, if you have a slight trace of an accent then you are not considered native and that is it. So even if you are in the first 1% of the foreign speakers you are going to be acknowledged for your achievement, but nevertheless categorized into the group of foreign sounding people.
If you are curious you can go and read what the scientific articles say about it. I think it is evident that there is a cut off age which changes from person to person, but it is somewhere between 9 and 15 or so. It is fairly easy to see in immigrant families who move with their children, provided the adults already know the language. Several years later the children would have no foreign accent and the adults will have it forever. Interesting that even Tesla who was pretty young (late twenties) when he came to the USA kept his accent all his life, so it is not a matter of intellect or immersion, it is what the brain can and can't do after certain age.
There is one interesting factor though: from which native language you come and which language you try to learn. Sometimes the pronunciation is so vastly different that success is fairly limited after certain point. You can try and do what you can do, but be realistic. Maybe picking the right language for your native background is already half the battle. There is one more thing. Not all languages are so obsessed with accent correctness. I believe that English is particularly biased based on accent compared to more phonetic languages like Spanish, Italian, some from the Slavic family and possibly others. This comes from the fact that in English a lot of the meaning is heavily dependent on the actual pronunciation and native people who are mono lingual are really having hard time to understand when there are some differences in speech.