We present the construction and performance of an ultra-low temperature scanning tunneling microscope (STM), working in ultra-high vacuum conditions (UHV) and in high magnetic fields up to 9 T. The cryogenic environment of the STM is generated by a single shot $^3$He magnet cryostat in combination with a $^4$He dewar system. At base temperature (300~mK), the cryostat has an operation time of approximately 80 hours. The special design of the microscope allows the transfer of the STM head from the cryostat to a UHV-chamber system, where samples and STM-tips can be easily exchanged. The UHV chambers are equipped with specific surface science treatment tools for the functionalization of samples and tips, including high-temperature treatments and thin film deposition. This, particularly, enables spin-resolved tunneling measurements. We present test measurements using well known samples and tips based on superconductor and metallic materials such as LiFeAs, Nb, Fe and W, respectively. The measurements demonstrate the outstanding performance of the STM with high spatial and energy resolution as well as the spin-resolved capability.