。
The moment she stepped into her room, she started crying.
Literal
She [topic-は] her own room [into-に] entered [the instant-とたんに] cried-began.
~たとたんに attaches to a past-tense verb to mean 'the very instant X happened, Y followed immediately.' 泣きはじめる is a compound verb (泣く 'cry' + 始める 'begin'); ~始める is the standard auxiliary marking the inception of a continuing action. Compared to 泣き出す ('burst into tears'), 始める emphasizes the onset's start, while 出す implies a more sudden eruption.