The laws of this land do not shield public figures just criticism, but they do protect them against what?

Theoretically they are protected against libel and slander.

http://legal-dictionary.thefreedictionary.com/Libel+and+Slander

The laws of most lands, including democratic societies, provide a certain level of protection to public figures. While public figures may face criticism due to the nature of their positions, there are certain legal safeguards in place to protect them against various risks. These protections are generally aimed at striking a balance between freedom of speech and the right to privacy or reputation.

One key protection is defamation laws. Defamation refers to making false statements about someone that harm their reputation. Public figures, such as politicians, celebrities, or government officials, often have a higher burden of proof in defamation cases compared to private individuals. To prove defamation, a public figure must demonstrate that the statement made about them was not only false but also made with "actual malice" or with a reckless disregard for the truth.

Furthermore, public figures are also protected by laws regarding privacy. While public figures have a diminished expectation of privacy compared to private individuals due to the inherent nature of their positions, they still have certain rights. These laws prohibit the unauthorized disclosure of private personal information, intrusion into their private lives, and invasion of their personal space.

Moreover, public figures may be protected against harassment or threats through laws related to stalking, cyberbullying, or hate speech. Such laws aim to prevent the targeted intimidation or harassment of public figures both online and offline.

It is important to note that the specific legal protections offered to public figures may vary from country to country, as laws differ across jurisdictions. Therefore, it is essential to consult the specific laws in your jurisdiction to fully understand the protections available to public figures.