Shinzoo ga tsuyoi describes a socially bold, cheeky person. Usually considered a negative trait, the phrase also may refer to having the courage (or gall) to behave against what is normally expected, like an employee who questions his boss, or a student who challenges the teacher.
(Style: spoken/casual/A=female, B=male)
A: Sachiko-san, daijoobu kashira. Minna o daihyoo shite fuhei o ji ni itta kedo.
B: Kanojo nara daijoobu sa. Shinzoo ga tsuyoi kara hakkiri monku ieru daro.
A: I wonder if Sachiko is OK. She went to register a complaint on behalf of the group.
B: She’ll be fine. She has a lot of nerve; she’ll tell them exactly what they did wrong.