<p>This study explores a predator-prey model operating in continuous time. The model incorporates a density-dependent mortality term for the predator population that reflects the influence of a double Allee effect. The proposed model is investigated analytically and numerically, with a particular focus on the impact of both the Allee effect and the density-dependent mortality. The analysis reveals that the system can exhibit bi-stability when coexistence equilibria exist. Interestingly, the model can even exhibit tri-stability, characterized by the presence of two stable coexistence equilibria, along with a stable predator-free equilibrium point. The ecological implications of bubbling and hydra phenomena within the system are thoroughly examined. Due to the double Allee effect, the emergence of bubbling cycles, characterized by increasing and decreasing amplitudes, is explored. All possible local bifurcations are identified and illustrated using one- and two-parametric bifurcation diagrams. A sensitivity analysis is performed to investigate how key parameters affect the biomass balance of the interacting species. Furthermore, diffusion-driven instability analysis is employed to derive pattern formation conditions for the predator-prey system. Numerical simulations are conducted to reveal rich Turing patterns with complex self-organized structures under the combined influence of diffusion and the Allee effect in the spatiotemporal domain. The simulations demonstrate a gradual dynamical shift from diffusion-driven patterns to Allee effect-driven patterns as the Allee parameters are adjusted. Additionally, the classification of irregular patches within the spatiotemporal dynamics allows for the identification of non-Turing patterns that may arise. Finally, the proposed reaction-diffusion framework provides a unified setting for investigating complex dynamical behaviours such as bubbling and hydra effects and offers new insights into their spatiotemporal manifestations.</p>