。
The news made her feel like crying.
Literal
She [topic-は] that news [object-を] heard-and want-to-cry mood [in-に] became.
~たい気分になる ('come to feel like doing X') stacks several pieces: the want-form ~たい ('want to'), the noun 気分 ('mood, feeling'), and になる ('become'). The whole phrase describes drifting into a particular emotional inclination rather than acting on a settled desire — fitting for ambient feelings like wanting to cry, wanting to be alone, wanting to skip work. Compare 泣きたい (bare 'want to cry'), 泣きそう ('on the verge of crying'), 泣きたい気分 ('in a crying mood'): a spectrum of subjective states distinguished by what they emphasize.