You will have to seek a court order. You can get one by filing a lawsuit against the unknown defamer, then submitting a subpoena to Instagram for the identity, which they probably won't comply with, then you will need to bring a motion to compel. Then, after all that, you will get the info.
You should try to get Instagram to agree to take the offending profile down. Talk to them first, it will probably be easier, cheaper, and faster.
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