I know that in order for a GPS to be used under IFR (that is shoot GPS approaches under IMC) it must meet certain TSO requirements, and must be RAIM capable. Are there any handheld GPS that are IFR approved to do as mentioned above.
No. It is impossible for handheld GPS units to meet the cert. criteria. One of the requirements is that they must drive an external CDI, such as a HSI or OBS. It is not exciting reading, but the AIM details some of the requirements.