。
She studied English as hard as she possibly could.
Literal
She [topic-は] as-much-as-possible wholeheartedly English [object-を] studied.
できるだけ (as much as possible) and 一生懸命 (with all one's might) stack to emphasize maximum effort. 一生懸命 — literally 'one life, at risk' — is one of the most common Japanese expressions for giving something your all. できるだけ sets the upper bound ('as much as she could'), while 一生懸命 describes the intensity of effort within that bound. Together they create an emphatic statement about dedication to language study.