Massive early-type galaxies follow a tight relation between the mass of their central supermassive black hole (MBH) and their stellar mass (M⋆). The origin of observed positive outliers from this relation with extremely high MBH (> 109 M_{⊙ }) remains unclear. We present a study of such outliers in the Hydrangea/C-EAGLE cosmological hydrodynamical simulations, designed to enable the study of high-mass galaxy formation and evolution in cluster environments. We find 69 MBH(M⋆) outliers at z = 0, defined as those with M_BH> 107 M_{⊙ } and MBH/M⋆ > 0.01. This paper focuses on a sample of five extreme outliers, that have been selected based on their MBH and M⋆ values, which are comparable to the most recent estimates of observed positive outliers. This sample of five outliers, classified as `black hole monster galaxies' (BMGs), was traced back in time to study their origin and evolution. In agreement with the results of previous simulations for lower mass MBH(M⋆) outliers, we find that these galaxies became outliers due to a combination of their early formation times and tidal stripping. For BMGs with M_BH> 10^9 M_{⊙ }, major mergers (with a stellar mass ratio of μ > 0.25) at early times (z > 2) precede the rapid growth of their supermassive BHs. Furthermore, the scatter in the relation between MBH and stellar velocity dispersion, σ, correlates positively with the scatter in [Mg/Fe](σ). This indicates that the alpha enhancement of these galaxies, which is closely related to their star formation history, is related to the growth of their central BHs.