These are the instructions to root Samsung Galaxy S3 Mini GT-I8190 using pre-rooted Stock Rom (android 4.1.2 base-XXAMG1).
Requirements: Your Samsung Galaxy S3 Mini GT-I8190 should have at least 30-40 percent of battery to perform the rooting process.
Step 1: Download and Install Samsung USB Driver on your computer. If in case, Samsung USB Driver is already installed on the computer then SKIP this Step.
Step 2: Download and extract the root files on your computer. After extracting you will be able to see the following files:
Step 4: Now, you have to enter into Download Mode on your phone by Pressing Volume Down Key, Home Button and Power key at same time for 5-8 seconds until you entered to the download mode.
Step 6: Now, Open Odin3 (found in the extracted folder, that you have downloaded in the Step#2) on your computer. Then connect your phone to the computer.
Step 8: Once your device detected by Odin, click on the PDA button and select the I8190OXXAMG1 PRE-ROOTED.tar file (you have extracted this file in step#2).
Step 9: Now, click on the Start button in odin to begin the Flashing. Once flash process is completed your phone will restart automatically.
Optional: You can also verify the root status of your device by using the Root Checker App.
[*] Data Loss Process: Flashing Pre-Rooted Stock ROM is always a data loss procedure. So, always take backup of your personal data before flashing the Stock ROM.
[*] Warranty Void: Your Samsung Galaxy S3 Mini GT-I8190 Warranty may be Void after following the above tutorial.
[*] How to Unroot? To unroot Open SuperSU > Settings > Full Unroot.
[*] Samsung Stock Firmware: If you are looking for the original firmware for your device, then head over to Download Samsung Stock Firmware page.
[*] Samsung USB Driver: If you are looking for the original USB Driver for your device, then head over to Download Samsung USB Driver page.
[*] Credits: The Pre-Rooted firmware used in this tutorial is made available by Avicohh (xda developer). Very thanks for the firmware, without it the above tutorial was not possible.