She grew more and more beautiful.

Literal

She [topic-は] increasingly beautiful became.

ますます is a reduplicated adverb of progressive intensification — the doubled form is its only form. Reduplication is one of Japanese's favorite ways to mark intensification or repetition, and it shows up across mimetics (ぴかぴか, ふわふわ), reduplicated nouns (人々, 山々), and adverbs like ますます and いよいよ. The な-adjective shape would be 美しく (the く-form of the い-adjective 美しい) plus なる ('become'), giving the standard 'become beautiful' pattern.