"Shot at" can be replaced with several other phrases that convey a similar meaning. "Attempted" is a good synonym to use when someone is making a try or effort to do something. Another phrase that can replace "shot at" is "took aim at," which implies that someone had a clear target in mind. "Fired upon" is another synonym that suggests violence or hostility in actions taken towards someone or something. "Assailed" can also be used in instances where someone is attacking or criticizing aggressively. Lastly, "tried to hit" is another useful synonym when describing someone's aim or attempt to strike an object or a person.