She did everything she could for me.

Literal

She [topic-は] my [as-much-as-できる限りの] thing [object-を] did [for-me-くれた].

私のできる限りの事 is a compact relative clause meaning 'everything that I/she could do' — 私の here turns ambiguous: it could mean 'my' (the speaker's possible actions, that she carried out) or, more naturally, 'on my behalf' (everything within her ability for me). The phrase ~の限り ('to the extent of, as much as') is the key grammar — できる限り means 'to the extent possible.' くれた marks the action as inward (toward the speaker), with appreciation. The whole sentence is a textbook expression of gratitude: 'she went above and beyond for me.'