In the context of the High-Luminosity LHC project at CERN, a platform has been developed to support groups needing to host electronics in radiation-exposed areas. This platform, called DI/OT, is based on a modular kit consisting of a System Board, Peripheral Boards and a radiation-tolerant power converter, all housed in a standard 3U crate. Groups customise their systems by designing Peripheral Boards and developing custom gateware and software for the System Board, featuring an IGLOO2 flash-based FPGA. It is compulsory for gateware designs to be radiation-tested in dedicated facilities before deployment. This process can be cumbersome and affects iteration time because access to radiation testing facilities is a scarce commodity. To make customisation more agile, we have developed a radiation-tolerant System-on-Chip (SoC), so that a single gateware design, extensively validated, can serve as a basis for different applications by just changing the software running in the processing unit of the SoC. HydRA (Hydra-like Resilient Architecture) features a triplicated RISC-V processor for safely running software in a radiation environment. This paper describes the overall context for the project, and then moves on to provide detailed explanations of all the design decisions for making HydRA radiation-tolerant, including the protection of programme and data memories. Test harnesses are also described, along with a summary of the test results so far. It concludes with ideas for further development and plans for deployment in the LHC.