Yoko danced with a grace that astonished everyone.

Literal

Yoko [topic-は] everyone [subject-が] be-surprised [like-ような] grace [with-で] danced.

~ような ('like / such that') attaches to a clause to produce 'a [noun] of the kind that [clause].' みんながびっくりするような = 'of the kind that would surprise everyone.' で marks the manner — 'with grace' as instrumental means.