She suddenly burst into tears when she heard the news.

Literal

She [topic-は] that news [object-を] heard-and, suddenly began-to-cry.

~だす is a compound auxiliary marking the abrupt onset of an action — 'burst into / suddenly start'. Distinct from ~始める ('begin to'), which is neutral, ~だす specifically carries surprise, suddenness, or involuntary onset. 泣きだす captures the moment of crying breaking out, the way 笑い出す captures bursting into laughter. 急に reinforces the suddenness adverbially — though it overlaps with ~だす, the doubling is natural in narrative for emphasis.