The easiest start is to find a good accent reduction and pronunciation coach to have the initial assessment and understand your unique path.
Unfortunately one often finds that even the basic vowels you think you had nailed down might be "wrong" and have to be corrected in order to have an easily understood and enjoyable articulation.
For a long time I couldn't even hear a difference between IPA [i] and [ɪ]. It took a few weeks to properly recognize and replicate them in English.
Couple of my favorite resources: https://www.youtube.com/channel/UC-MSYk9R94F3TMuKAnQ7dDg https://www.youtube.com/user/rachelsenglish/videos https://www.youtube.com/channel/UCv8YBYZ2s_imUC3H84FwVFQ
Under my point of view I view keeping your accent as part of your identity and something that makes you unique.
You’re unlikely to sound like a native but it’s also not really needed. English is a really mixed up language and we (native speakers) are used to diversity.
There’s actually a huge variations between different regions of the UK let alone native speakers from the rest of the world. So feel confident that it’s OK to retain your own accent as long as it’s not so strong it stops people from understanding you.
If for some reason you did manage to adopt a regional English accent then we’d actually find that quite funny. :D