The propagation of matter waves in curved geometry is relevant for ion transport, atomtronics and electrons in nanowires. Curvature effects are usually addressed within the adiabatic limit and treated via an effective potential acting on the manifold to which the particles are strongly confined. However, the strength of the confinements that can be achieved experimentally are limited in practice, and the adiabatic approximation often appears too restrictive for realistic guides. Here, we work out a design method for 2D sharply bent waveguides beyond this approximation using an exact inverse-engineering technique. The efficiency of the method is confirmed by the resolution of the 2D nonlinear Schrödinger equation in curved geometry. In this way, we realize reflectionless and ultrarobust curved guides, even in the presence of interactions. Here, the transverse stability is improved by several orders of magnitude when compared to circular guides of similar size.