Flow of viscoelastic polymer solutions in curved channels exhibits instability caused by the elastic nature of polymers even at low Reynolds numbers. However, scaling of the onset of this purely elastic instability in semidilute polymer solutions has not been previously reported. Here we experimentally investigate the flow of highly elastic polymer solutions above their overlap concentrations using pressure measurements and particle image velocimetry. We demonstrate that the onset of instability can be scaled by including shear dependent rheological properties of the polymer solutions in the nonlinear stability analysis. As a result, a universal criterion as function of normalized polymer concentration is provided for scaling the onset of purely elastic instability in the semidilute regime regardless of the type and molecular weight of the polymer.