。
She raised her children with tremendous effort.
Literal
She [topic-は] tremendous [genitive-の] effort [object-を] doing children [object-を] raised.
大変な is the na-adjective use of 大変, meaning 'serious / major / tremendous,' modifying 努力 ('effort') as a prenominal attribute — 大変な努力 ('a tremendous effort'). Distinct from the homographic adverbial 大変 ('very, extremely'), which attaches directly to predicates without な. 努力をする is the standard 'make an effort' collocation; the more compact 努力する ('strive') is also possible.