One of the most common requests from my ESL clients is "I want to improve my English pronunciation. I want my accent to sound more (in this case) American." There are practices I recommend to my ESL clients to improve their English pronunciation on their own, and if they wish, to modify their English accent to sound more like a native-English-speaker in this region.
Sir Sidney Poitier, known for his role in the movie To Sir with Love and many other movies, faced a similar issue early in his acting career. He wanted to be rid of his Bahamian accent in order to succeed in his acting career (it was a time when diverse accents were well less received.) To do this, he bought a radio, chose a program he liked, and imitated the accent of the host. He did this for 6 months, then audition for a part. That's how he got started in the movie industry.
What can we learn from Sidney Poitier? He chose someone who has clear pronunciation. The host was on radio. He had to speak clearly! So choosing someone with the kind of clear pronunciation and accent you want to imitate is a start.
Then Sidney imitated the host. Inflection, clarity, everything. He kept at this until the new speaking style became a part of him.
One of the elements in this kind of imitation is music–music of a language. You have listened to people speaking English with a British, Australian, Hawaiian, Indian, Chinese, Japanese, Spanish accent, right? Why is it easier to understand some and not others?
Have you ever listened to a song played by a different artist, arranged differently, and you hardly recognize the song until half a minute later? Maybe some of the notes were played slightly longer in one version or with a different instrument. The small change is all it takes to make you wonder "Is this the same song" for a moment.
Same with language. Some languages are spoken with more staccato. Some sound more melodic. Some put the inflection at the end of a sentence instead of the middle.
So when you start imitating someone whose accent and pronunciation you like, observe the length of the syllables, where is the inflection placed, when does the voice go up, and when does it come down. When you begin, just listen. When you have become accustomed to the music of this person, then start imitating.
Once you have mastered the imitation, you can find another person to imitate so you expose yourself to different styles. When you feel ready, you will come up with your own style that is both clear and that feels right to you.
Have fun with this. Just play with sounds. Don't make it about correctness. Language is about communicating your message.