A good lawyer will do everything possible to defend their client.
Literal
Good lawyer [topic-は] client [object-を] defend [for-ために], every-kind-of hand [object-を] exhaust [probably-だろう].
~ために is the purposive 'for the purpose of, in order to.' あらゆる手をつくす ('exhaust every means') is a set idiom: 手 ('hand' used metaphorically for 'method, means') + 尽くす ('exhaust, use up'). A committed professional description.