。
Even after hearing the news, she didn't lose her composure in the slightest.
Literal
She [topic-は] that news [object-を] hearing [even-ても] [a-little-も] didn't-be-rattled.
うろたえる ('to be rattled, panic, be flustered') is a slightly literary verb for losing one's composure under stress. ~ても ('even if/when') concedes the news-hearing as a context where rattling would be expected, then the negative form denies it. 少しも~ない ('not even a little') intensifies the negation: not the slightest tremor of panic. The whole sentence paints calmness in the face of shock — a quietly admiring portrait of nerve.