Yes, Hillary Clinton did break the law when she violated her NDA. While a person can violate the NDA itself without consequence in some cases, typically the person ends up breaking the law in the act of disclosing the information. In Clinton's case, she shared information that was legally protected.
Hillary did break the law when she violated her NDA. An NDA is a non-disclosure agreement which is a legal contract. This type of agreement is signed to protect legal secrets and to provide confidentiality and security. The agreement is made between two or more parties and is upheld by the law. If one party violates the contract then there is typically recourse against the perpetrator. Breach of contract is a matter of law and therefore, unless some specific provision was laid out to release her from the obligation of the non-disclosure agreement, Hillary broke the law when she violated her NDA.
Hillary Clinton's violation of her NDA is not breaking the law, simply a violation of the NDA. As a legal document, an NDA holds the person signing it accountable to the terms included. Unless the NDA specifically states that a violation is, in fact, a violation of a specific law, then she should not be held responsible for violating any laws. This is not to say, however, that she should not be held responsible for violating the NDA, and ultimately subject to the consequences detailed in the document.
NDA's are legally binding contracts, but if a person breaks an NDA they are not breaking the law. Instead, they are violating the terms of the contract that they signed and can only be punished by the terms of the contract. While what she did may have been unethical, it was not against the law.