State-of-the-art technologies for wind and tidal energy exploitation focus mostly on axial turbines. However, cross-flow hydrokinetic tidal turbines possess interesting features, such as higher area-based power density in array installations and shallow water, as well as a generally simpler design. Up to now, the highly unsteady flow conditions and cyclic blade stall have hindered deployment at large scales because of the resulting low single-turbine efficiency and fatigue failure challenges. Concepts exist which overcome these drawbacks by actively controlling the flow, at the cost of increased mechatronical complexity. Here, we propose a bioinspired approach with hyperflexible turbine blades. The rotor naturally adapts to the flow through deformation, reducing flow separation and stall in a passive manner. This results in higher efficiency and increased turbine lifetime through decreased structural loads, without compromising on the simplicity of the design.