。
She boasts about having been beautiful when she was young.
Literal
She [topic-は] young time [at-に] beautiful was [nominalizer-こと] [object-を] is-boasting.
自慢している (is boasting) with ~ている marks this as an ongoing behavior — she regularly brings up her past beauty. 若い時に美しかったこと nominalizes the whole past experience with こと: 'the fact of having been beautiful when young.' The sentence carries a faintly unflattering tone — 自慢する (to boast) implies she brings it up too much.