Hydrodynamics is an effective theory of a many-body system at length and time scales much larger than those of the underlying microscopic dynamics. Traditionally, hydrodynamics has been thought to be applicable only when the system is near equilibrium. However, recent experiments in ultra-relativistic heavy-ion collisions and cold atomic systems have revealed that hydrodynamics can work even in far from equilibrium conditions. The discovery of hydrodynamic attractors has opened the door to the theoretical understanding of the applicability of hydrodynamics in far away from equilibrium conditions and has been influential in the study of the phenomenology of QGP produced in heavy-ion collisions. However, in the latter case, we need to consider both weakly interacting and strongly interacting degrees of freedom. In our work, we study how hydrodynamic attractors can also emerge in such a complex system involving flow of hybrid degrees of freedom. To this end, we use the hybrid twofluid model developed by Kurkela et al to couple two viscous fluids, one strongly coupled and other weakly coupled, via democratic metric couplings. In this model, the interactions between its two sectors are encoded by their effective metric backgrounds, which are determined mutually by their energy-momentum tensors such that the full energy-momentum tensor is conserved in the physical background. We find that the hybrid system exhibits a 2D attractor surface in 4D phase space of appropriate hydrodynamic variables. One of the key findings of our work is that the energy distribution between the two systems evolves at early times quite similar to the bottom-up thermalization scenariao of Baier at al. while we gain new insights into how initial conditions affect hydrodynamization of the composite system.