The trial lawyers couldn't get around the silent-treatment tactics used by the Mafia boss.
Literal
Court-lawyers-[plural-達] [topic-は] Mafia [possessive-の] boss [subject-が] use silent-treatment tactics [object-を] dodge [could-ことができなかった]
Several pieces. 法廷弁護士 = trial lawyer, barrister (as distinct from consulting lawyer). The plural suffix ~達 gives 弁護士達. マフィアのボスの用いる is a relative clause modifying 黙秘戦術 (silent-treatment tactic) — the second の is the subject marker inside the relative clause, equivalent to が. 黙秘 is the right-to-remain-silent concept in legal contexts. かわす = to dodge, parry, evade.