Not hardly is a hardy colloquialism that has been in English a long time and is likely to stay, but it might be considered out of place in serious writing. Because hardly means barely or almost not, adding the modifier not creates a double negative. Taken literally, not hardly would mean definitely or very. In practice, though, not hardly means the same as hardly.
Writers often use not hardly to create a colloquial tone. In many of the examples we found, not hardly is a standalone sentence—for example:
Is this an ideal solution? Not hardly. [NJ.com]
Can I talk to them directly on the phone? Not hardly. [letter to Chicago Tribune]
Not that anyone admitted the importance of the moment. Not hardly. [Register-Guard]
In each of these cases, hardly would convey the same meaning as not hardly, but it wouldn’t have the same folksy tone.