The main one is literally called "crime against peace" in which any war of aggression without sufficient justification of self-defense is considered a breach of international law wiki. It was first codified in Principle VI of the Nuremberg Principles following WW2 and also incorporated into the Charter of the United Nations (Article I, US is a founding member), Charter of the Organization of American States (Article III, US is a founding member) as well as the International Criminal Court (Article 8; "Crime of Aggression", US is not a signatory). While US government has argued that it was acting in self-defense, here is a legal analysis on why that claim probably cannot stand up to scrutiny "The Legality of the United States Invasion of Panama" by John Quigley (1990).

There is no "international law" in the sense you are asking about. That is to say there is no single "Book of International Law" that spells out the types of offenses and the elements of the crime that must be proven.

Rather, the phrase "international law" refers to a collection of treaties, principles, conventions, and ideas that govern what international relations should look like. Normally when people say a country's war is "illegal" they mean it violates the UN Charter, which specifies under what conditions war is justified. It was also claimed to be contradictory to the Charter of the Organization of American States, and some people have argued that Panama's provocations did not meet the criteria to justify military action.

Whether this is synonymous with "unjustifiable" is an entirely separate question. Given that the leader of Panama declared war on the United States, I have a hard time comprehending in what way it was illegal.

Quite often in politics, when someone says something was "against international law" what they really mean to say is, "I disagree with it."