"A beleaguered city" is a term used to describe a city that is under siege or facing extreme difficulties. There are several synonyms that can be used to describe such a situation. One such word is "besieged," which implies that the city is under attack or surrounded by an enemy force. Another similar term is "embattled," which suggests that the city is caught up in a fierce struggle or conflict. "Under duress" is another option to use to describe a city facing immense pressure and threats. In summary, there are several synonyms available to accurately depict the difficult situation of a beleaguered city.