Acoustic vibrations in plasmonic nanoparticles, monitored by an all-optical means, have attracted significant increasing interest because they provide unique insight into the mechanical properties of these metallic nanostructures. Al nanostructures are a recently emerging alternative to noble metal nanoparticles, because their broad wavelength tunability and high natural abundance make them ideal for many potential applications. Here, we investigate the acoustic vibrations of individual Al nanocrystals using a combination of electron microscopy and single-particle transient extinction spectroscopy, made possible with a low-pulse energy, high sensitivity, and probe-wavelength-tunable, single-particle transient extinction microscope. For chemically synthesized, faceted Al nanocrystals, the observed vibration frequency scales with the inverse particle diameter. In contrast, triangularly shaped Al nanocrystals support two distinct frequencies, corresponding to their inand out-of-plane breathing modes. Unlike ensemble measurements, which measure average properties, measuring the damping time of the acoustic vibrations for individual particles enables us to investigate variations of the quality factor on the particle-to-particle level. Surprisingly, we find a large variation in quality factors even for nanocrystals of similar size and shape. This observed heterogeneity appears to result from substantially varying degrees of nanoparticle crystallinity even for chemically synthesized nanocrystals.