To do any sort of modding on your Samsung galaxy core, you will need to download and install CWM clockworkmod recovery. While with the stock recovery, you can wipe your phone, clear cache, with the CWM recovery, you can install custom ROMs, make Nandroid backup and even partition your SD card.
Before you proceed, ensure that, you have 30 percent or more battery. Copy Recovery.tar File In ODIN Folder. Open settings on your phone and go tot developer options > tick USB Debugging. Now, turn off your phone.
Now, go into download mode. You can do that by pressing and holding the Volume Down + Home Key + Power Key. Do that for few seconds until download screen comes up. Press Volume Up key to proceed.
Connect your phone via USB cable and open ODIN. Click on PDA button and select recovery.tar file. Press the start button to start the process. It should display pass.