All applicants must meet character requirements when they apply for a visa. The character requirements not only relate to previous criminal history, but include any issues the applicant might have had with any immigration departments in any country, having been subjected to any police investigations, etc.
The requirements are slightly different depending on whether you are applying for a temporary visa (e.g. visitor, student, work visas) or whether you are applying for residence. The standard is more stringent with residence visa applications.
It is important to remember that you must declare any relevant information upfront, because if Immigration New Zealand finds out later that you might have intentionally hidden something from them, it will become an uphill battle to pursuade them otherwise. Depending on what character issues you might have, such issues might deem you outright ineligible, or ineligible unless character waiver is granted.
If you need to request a character waiver to Immigration New Zealand, it would be advisable to seek professional assistance, because if you are unable to resolve the issues fully, you will continue to have problems down the track with all future immigration applications.