。
She, a singer? No way!
Literal
She [subject-が] singer is [such-as-なんて] absolutely-not.
とんでもない expresses strong dismissal — 'absurd, outrageous, no way, far from it.' Combined with ~なんて ('the very idea of X'), it forms a punchy exclamation: 'her, a singer? Nonsense!' Note the が rather than は on 彼女 — the focus particle here marks her identity as the surprising/contested element. なんて is a useful dismissive marker: it adds an undertone of 'such a thing as,' often with a flavor of disbelief or disdain. The whole sentence is a vivid spoken outburst.