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She refuses to fly because she's afraid of crashing.
Literal
She [topic-は] crash [object-を] fearing plane [to-に] ride [won't try-ようとしない].
~ようとしない ('won't try to / refuses to') expresses persistent unwillingness — not just a one-time refusal but an ongoing stance. 墜落を恐れて ('fearing a crash') uses the te-form of 恐れる to set up the reason for the refusal. 飛行機に乗る ('to board a plane') is the standard way to say 'take a flight.'