You probably can't :) I write Nicelocal reviews all the time, and if I don't like something about a business, I'm not shy about it. All my Nicelocal reviews are still up, so I'm pretty sure Nicelocal doesn't take down negative reviews for money. My only suggestion is to improve your service and leave a tasteful responses to the negative Nicelocal review :)

My advice is to write a detailed response to this review and apologize on behalf of your company. Then other clients will see you care about your reputation. You could also offer this client some kind of free service in exchange for deleting the Nicelocal review themselves or at least marking the problem as resolved.

You can try to get the review deleted, of course. But first you need to have a premium account, which costs money. But that doesn't mean the moderators will delete a negative comment right away as long as you pay up. You need to prove the Nicelocal review was biased. Otherwise they won't delete the review. I know from personal experience that this can be pretty tough to do. If the mods have any doubts about your claim, they probably won't delete the Nicelocal review.