Hiya!
I'm a multilingual person whose English is 3rd language but I try my best to answer.
I will say very straightly that completely rigging off from "foreign" accent is actually very tuff and I do think that accent is a much more complex thing than just pronunciation, it's also a "melody" of sounds, intonations... Even from foreign people who have study Japanese hard and spoken Japanese from decades or few years, I can still hear their original accent weakly while speaking (of course, these people accent is much better than those who just started learning the language but it's still there).
When I was small, I thought that in Japanese accent is perfect because everyone praised in Japan and Finland how good my Japanese accent was/is and not sounding "foreign" (I am Finnish-Japanese, my mom is Japanese). Actually, this is little true because I was like 5 years old and under when my family lived in Tokyo and my mother always talked me in Japanese every single day and watched some anime, read manga etc. But the real truth is that I have a slight Finnish accent in my Japanese, it is definitely weak but still, it is in there. I realised this when I started UTAU, recorded a Japanese VB and didn't take too long until my UTAU was labelled as "Oversea UTAU" by a Japanese UTAU community in NND plus I started to listen to natives VB and soon realized that my accent/melody was different than theirs e.g. my main UTAU Aki's "a" and "w/v" can sometimes sound more like Finnish than Japanese. Also, my Finnish VCV has also a weak Japanese accent in especially in a vowel "a", someone even came to ask me what is the "correct" pronouncing of Finnish "a" because in some samples it sounded center like in Japanese or back or very open etc... I hear from this particular person that Aki has 3 ways to say "a" (LOL). Now when I listen to it, it's actually very accurate. I didn't realize this because how used to I was my own accent XDD
Ok, my point is that don't worry about accent too much - especially if isn't your mother tongue because guess what: everyone has it! British and American sounds different, people from Tokyo sounds different than people from the countryside, from same city elder people accent can be different than a youth etc.
Good accent comes from good/correct pronunciation, a lot of speaking practicing and listening to it (music and regular talking shows). Try imitate natives say specific phrases/words/sentences aloud, listen to the tempo, how they rhythm syllables, watch lip movement etc. Getting to sound like Japanese takes a lot of time and effort, so I suggest to starting off focusing mainly on pronunciation from the beginning as getting pronouciation good is less time taking than "rigging off" from an accent. As long as you're actually trying your best with your current skills, people will be understandable and if you have done well, they can even praise you a bit even if it was little off in few parts.
As being English speaker (I assume that you are English speaker), you know plenty of vowels/consonants by default, so learning pronouncing other languages is will be less or more like alternative your current set of vowels/consonants and in general, not many new sounds to be learned from completely scratch.
VOWELS
For English speakers, I advise to watch out to not pronounce "o" as English diphone "ow" and with "a" to not making in "back" of your mouth. Japanese "a" should be pronounced more central/middle of your mouth and mouth should be more open in Japanese "a" than in English one.
CONSONANTS
- With consonants, learn to make less aspiration or not aspiration at all in k/t/p.
- Japanese "w" is not same that English "w", Japanese "w" have a little lip compressing, maybe try to think Japanese "w" to be a child between English "w" and "v"(?)
- Japanese "sh" sound, again it's not same than English "sh". If you want to know how to pronounce Japanese "sh" properly google "how to pronounce Chinese x" because Chinese "x" sound is same than Japanese "sh" and many actually great advises/resources available for Chinese x for English speakers TBH.
- Japanese "r" is basically a child between English "l" and "d". Please, don't do English "r" as sounding too "back". If you cannot do Japanese "r" right away, don't give up! Practice, practice, practice... You can pronounce Japanese "r" as English "l" as a beginner and if fact some Japanese singers R tend to sound very L-ish while singing, so that's pretty ok especially in UTAU IMO I know that some people will disagree with this opinion but to be very honest L sound is much closer than English R because where tongue is placed inside mouth.
Fun fact: Sometimes when Japanese man swears or being angry, you might hear they trill their "r" like Spanish "rr" and many Japanese think that trilling r sounds are cool and for them sounds like you're strong BUT please please PLEASE! Don't trill Japanese "r" sound by default, that sounds irritating and incorrect if all the time!
Fun fact 2: Some Japanese people incorrectly believe that English r=Spanish rr.
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I hope that you find this post helpful and good luck