。
She is terribly afraid of dogs.
Literal
She [topic-は] dog [object-を] greatly is-fearing.
恐れる ('to fear, dread') is the verb counterpart of the adjective 恐い/怖い. As a verb it takes its object with を (犬を恐れる), in contrast to the adjective construction 犬が怖い. Pairing it with ~ている produces a continuous-state reading ('lives in fear of dogs'). たいへん is an everyday intensifier — sturdier and slightly more grown-up sounding than すごく or とても. Compared with the more colloquial 怖がる, 恐れる carries a dignified, almost literary tone — better for genuine dread or formal fear of consequences.