。
She'd happily do anything for me.
Literal
She [topic-は] gladly me [for-のために] anything does [for-me-てくれます].
私の為に ('for my sake, for me') uses 為 (often written 為 or 用) plus the attributive の and the marker に — the pattern noun + のために for 'for the sake of.' 何でも ('anything, whatever') is the universal pronoun built from 何 ('what') + でも ('even, also'); the でも generalizes to 'no matter what.' Combine with 喜んで and ~てくれます (polite ~てくれる), and the sentence is a near-template for declaring devotion or willingness — common in formal speeches as well as melodramatic dialogue.