Dual-comb spectroscopy has become a powerful spectroscopic technique in applications that rely on its broad spectral coverage combined with high frequency resolution capabilities. Experiments to date have primarily focused on detection and analysis of multiple gas species under semi-static conditions, with applications ranging from environmental monitoring of greenhouse gases to high-resolution molecular spectroscopy. Here, we utilize dual-comb spectroscopy to demonstrate broadband, high-resolution, and time-resolved measurements in a laser-induced plasma. As a demonstration, we simultaneously detect trace amounts of Rb and K in solid samples with a single laser ablation shot, with transitions separated by over 6 THz (13 nm) and spectral resolution sufficient to resolve isotopic and ground state hyperfine splittings of the Rb D2 line. This new spectroscopic approach offers the broad spectral coverage found in the powerful techniques of laser-induced breakdown spectroscopy (LIBS) while providing the high-resolution and accuracy of cw laser-based spectroscopies.