In medical-related tasks, soft robots can perform better than conventional robots because of their compliant building materials and the movements they are able perform. However, designing soft robot controllers is not an easy task, due to the non-linear properties of their materials. Since human expertise to design such controllers is yet not sufficiently effective, a formal design process is needed. The present research proposes neuroevolution-based algorithms as the core mechanism to automatically generate controllers for biohybrid actuators that can be used on future medical devices, such as a catheter that will deliver drugs. The controllers generated by methodologies based on Neuroevolution of Augmenting Topologies (NEAT) and Hypercube-based NEAT (HyperNEAT) are compared against the ones generated by a standard genetic algorithm (SGA). In specific, the metrics considered are the maximum displacement in upward bending movement and the robustness to control different biohybrid actuator morphologies without redesigning the control strategy. Results indicate that the neuroevolution-based algorithms produce better suited controllers than the SGA. In particular, NEAT designed the best controllers, achieving up to 25% higher displacement when compared with SGA-produced specialised controllers trained over a single morphology and 23% when compared with general purpose controllers trained over a set of morphologies.