In recent years, the demand for solid, thin, and flexible energy storage devices has surged in modern consumer electronics, which require autonomy and long duration. In this context, hybrid supercapacitors have become strategic, and significant efforts are being made to develop cells with higher energy densities while preserving the power density of conventional supercapacitors. Motivated by these requirements, we report the development of a new high-performance dual-redox-mediator supercapacitor. In this study, cells were constructed using fully moldable buckypapers (BPs), composed of carbon nanotubes and cellulose nanofibers, as electrodes. We evaluated the compatibility of BPs with hydrogel polymer electrolytes, based on 1 mol L-1 H2SO4 and polyvinyl alcohol (PVA), supplemented with different redox species: methylene blue, indigo carmine, and hydroquinone. Solid cells were constructed containing two active redox species to maximize the specific capacity of each electrode. Considering the main results, the dual-redox-mediator supercapacitor exhibits high energy density of 32.0 Wh kg-1 (at 0.8 kW kg-1) and is capable of delivering 25.9 Wh kg-1 at high power demand (4.0 kW kg-1). Stability studies conducted over 10,000 galvanostatic cycles revealed that the PVA polymer matrix benefits the system by inhibiting the crossover of redox species within the cell.