This negotiation tactic is not a crime, but it does implicate an ethical rule for attorneys, Rule of Professional Conduct 4.5, which exists in some states, but has been dropped from the national model rules promulgated by the American Bar Association and is a controversial matter from state to state with several variant forms in different states. In Colorado, the relevant rule of professional conduct for lawyers (Rule 4.5 Threatening Prosecution) states:
(a) A lawyer shall not threaten criminal, administrative or
disciplinary charges to obtain an advantage in a civil matter nor
shall a lawyer present or participate in presenting criminal,
administrative or disciplinary charges solely to obtain an advantage
in a civil matter.
(b) It shall not be a violation of Rule 4.5 for a lawyer to notify
another person in a civil matter that the lawyer reasonably believes
that the other's conduct may violate criminal, administrative or
disciplinary rules or statutes.
The concern about the statement in the question is that mentioning that certain allegations would be put in a publicly filed complaint is an implicit threat to expose criminal acts of the other party if the other party doesn't cooperate, but to refrain from doing so if the other party cooperates. This violates Rule of Professional Conduct 4.5(a) above, and goes beyond Rule 4.5(b) above which states that it is not improper to simply tell someone that it may have been illegal and a crime to do the things that he did.
The critical distinction is the implied promise not to disclose these crimes publicly if the other party cooperates by not filing the proposed complaint.
Under Rule 4.5, a lawyer can tell someone that certain conduct is probably illegal, and can unilaterally report illegal conduct, but can't hold open the possibility of not reporting illegal conduct to gain a civil advantage. The theory is that it is contrary to public policy for a lawyer to put himself or his client in a position where he is promising to help cover up a crime or other violation of the law.
This is controversial, and is not adopted in all states, because it makes some very subtle distinctions that often hinge on strongly implied concepts, and that it provides benefit when applied in many cases to someone who has broken the law, instead of making their violation of the law something that makes them worse off in civil cases as well as in other contexts. There is not a counterpart to Colorado Rule of Professional Conduct 4.5 in the Rules of Professional Conduct of New York State, New Jersey, or Florida.
So, to the extent that this conduct is subject to ethical rules in any of these states, it would only be indirectly through, for example, through Rule of Professional Conduct 8.4 in each of these states, which is a general catch all clause prohibiting lawyers from committing culpable crimes or that is dishonest or that is prejudicial to the administration of justice. Rule 8.4 is the counterpart for lawyers of the substantive offense in military justice that a military officer has failed to comport himself as an officer and a gentleman. The history of the decision to remove an express prohibition on threatening prosecution from the ethical rules for lawyers is explained in a 2008 ABA article that also discusses how liability might arise under Rule 8.4.
In general, there is nothing wrong with making threats in a negotiation. Often that is precisely what negotiations are about. What is (arguably) wrong is making criminal, administrative or disciplinary charge threats in a civil lawsuit to gain advantage in a civil lawsuit. A prosecutor is perfectly free to make those threats in a criminal case, for example. Similarly, it is perfectly acceptable to make a threat of civil legal action, such as filing a lawsuit, in a civil matter, so long as it doesn't imply a threat to bring criminal, administrative or disciplinary charges if the other side doesn't cooperate.
Whether it is proper for an attorney to do this depends heavily upon the state in which this negotiation is taking place, which is not identified in the question.