There are several excellent alternative words and phrases that can be used instead of the term "best shot." If someone wants to describe the effort they are putting into something, they could use words like "maximum effort," "utmost," or "all-out." Alternatively, the phrase "giving it my all" is a popular way to convey the same idea. Other phrases that might work well include "top form," "optimum," and "peak performance." Whatever words are chosen, the aim should be to communicate the idea of someone striving to do their best and putting in a significant amount of effort to achieve their goals.