Testing within the sandbox only requires a simple registration at our website. The Sandbox is a closed environment, without any connection to the banks (API Providers), that retrieves static data with the same structure as production data. This way, a TPP can ensure that messages are well formated. No need to use eIDAS certificates or other credentials than register with us. 
The Test and Production environment provides all the technical documentation and end-to-end testing to fully test your apps and user experience. You need to be a registered TPP and have a valid eIDAS or at least have formally started a registration with a National Competent Authority (NCA) for using PSD2 APIs. For APIs out of PSD2 scope, requirements will depend on the Product.