The RPCS3 developers have streamlined this process significantly.
Navigate to the official PlayStation System Software Update page. Look for the "Download PS3 Update" button. The file will be named PS3UPDAT.PUP. Ensure the file size is approximately 200MB to 300MB. How to Install Firmware in RPCS3
If the download doesn't start, right-click the button and select "Save link as..." . The file will be named PS3UPDAT.PUP . 2. Install Firmware in RPCS3
If you try to run a game that requires a higher firmware version than what you have installed, the game may fail to boot or crash during the loading screen. You can simply repeat the installation steps above whenever a new update is released. Common Troubleshooting Tips