Modern FPGAs (Field Programmable Gate Arrays) are becoming increasingly important when it comes to embedded system development. Within these FPGAs, soft-core processors are often used to solve a wide range of different tasks. Soft-core processors are a cost-effective and time-efficient way to realize embedded systems. When using the full potential of FPGAs, it is possible to dynamically reconfigure parts of them during run time without the need to stop the device. This feature is called dynamic partial reconfiguration (DPR). If the DPR approach is to be applied in a real-time application-specific soft-core processor, an architecture must be created that ensures strict compliance with the real-time constraint at all times. In this paper, a novel method that addresses this problem is introduced, and its realization is described. In the first step, an application-specializable soft-core processor is presented that is capable of solving problems while adhering to hard real-time deadlines. This is achieved by the full design time analyzability of the soft-core processor. Its special architecture and other necessary features are discussed. Furthermore, a method for the optimized generation of partial bitstreams for the DPR as well as its practical implementation in a tool is presented. This tool is able to minimize given bitstreams with the help of a differential frame bitmap. Experiments that realize the DPR within the soft-core framework are presented, with respect to the need for hard real-time capability. Those experiments show a significant resource reduction of about 40% compared to a functionally equivalent non-DPR design.