We present a relative sensitivity of in-fiber inter-cross demodulation of a Mach-Zehnder interferometer (MZI) based on an etched multi-core fiber (eMCF). The sensor can measure the external refractive index (RI) and temperature with a large fringe visibility of 15 dB. It is tuned using a simple technique of slow chemical etching. When the outer cores of MCF will be exposed to the surrounding, a large difference of relative effective RI is observed, which enhances the sensitivity of the sensor. The sensor's wavelength and intensity responses have displayed that it can function with three different inter-cross-demodulation phenomena. A superior RI sensitivity of 178.20 dB/RIU in the range of 1.334 to 1.370, and temperature sensitivity of 66.73 pm/°C in the range of 30 to 80 °C are obtained, with an adequate linear response. Besides, it can readily resolve the issues of cross-sensitivity. Moreover, it has many advantages including easy fabrication, compact size, multiplex, repeatable, stable, and can easily differentiate RI and temperature, which lack others.