。
The storm raged with all its fury.
Literal
Storm [subject-が] as-much-as-possible [of-の] fury [object-を] wielded.
あらん限り ('as much as possible, utmost, all there is') uses the classical/literary negative ぬ form of ある (あらず → あらん) — a frozen archaic construction. 猛威 ('fury, ferocity') is a dramatic noun. 振るう ('to wield, to exert, to exercise') is used here metaphorically — 'to wield fury' = 'to rage.' A literary, vivid weather description.