Apprenticed to a Neapolitan dressmaker at thirteen, Dell'Acqua trained at the Accademia di Belle Arti in Naples before moving to Milan. He launched an eponymous line in 1996, showing his first prêt-à-porter at Milan Fashion Week, and shot campaigns with photographers including Juergen Teller and Steven Klein. Along the way he designed La Perla's first ready-to-wear line (2002–2008) and led Borbonese and, briefly, Brioni's womenswear.
Since 2010 he has run N°21, his own label, with Italian manufacturer Gilmar holding a stake since 2015 and a headquarters in Milan's Porta Venezia. He has also designed for Rochas, Les Copains and a capsule for Tod's — by 2022, a third of N°21's turnover came from Japan.