This is probably beyond what you want to hear, but here's my shot at your question:
If you really want to make it legal, you need to look up the zoning codes for your island. Each island will have different zoning districts such as: Ag, rural, residential, multi-family, business, etc... Then there are categories of uses for each zoning district such as "permitted uses", "accessory uses", "special uses", etc... The permitted uses are
things you can just do without any permits. In ag it would probably be along the lines of growing crops, raising livestock- basically uses that everyone expects on ag land.
Then there are the accessory uses. This may be a slaughterhouse, processing mill, fruit/vegetable packing plant- uses that are a little above and beyond what your typical ag owner would do, but still related to ag. Lastly, you have "special uses". This would be uses that are likely to occur on ag land, but don't really have anything to do with ag. Think paintball fields, camping grounds, bed and breakfast homes, and of course, firing ranges. With "special uses", you'll most likely need a special use permit.
The problem with a special use permit is you'll probably need to go all the way up to the Planning Commission, or maybe even the City or County Council for approval. So it's not going to be easy or cheap. In addition, you will have to notify your neighbors that you're planning on putting up a shooting range, so they will have a chance to testify for or against your project. Keep in mind if you do get approval, it also will have an expiration date, so at some point you'll have to renew it and go through a similar, albeit slightly quicker process all over again.
If you happen to go through all of that and get approval, the huge plus is you then you have a legitimate and legal range. It makes it that much harder for complaints if your range is legal and permitted. But as I said, this can be an expensive and timely process. The unfortunate thing about Hawaii laws is they don't account for the backyard shooter. The assumption is any firing range will be a Kokohead or Ukumehame type. Call your local Planning or Zoning Department for specific information because each County will have slightly different laws.
...or you skip all that, put up a backstop, heavily invest in some subsonic .22 ammo and have at it. Depending on the size of your lot, your neighbors might not even hear it.