Root without installing TWRP recovery...
Try on your own risk. On chinese version possible bootloop.

1. Download Magisk manager GitHub link or Xda link and install.
2. Download Redmi Note 8 Pro firmware exact same as your current MIUI version in my case BEGONIA EEAGlobal_V11.0.1.0.PGGEUXM. Settings-> about phone - to check your current MIUI version.
3. Unzip downloaded firmware and transfer boot.img to your phone by usb cable or any other method...
4. Run Magisk manager and sellect Install next to Magisk is not instaled in pop up menu select again Install then Select and Patch a File if any give permissions and select your boot.img file (see number 3. post). Patched boot.img file will be in Download folder after patching.
5. Download - [TOOL]Minimal ADB and Fastboot(Windows) link and extract desired location.
6. Copy/move patched_boot.img from Download folder[phone storage] to extracted ADB and Fastboot folder[PC] and rename it to boot.img
7. Run cmd-here.exe file and put following command fastboot flash boot boot.img and then fastboot reboot.


If you want go back to stock boot or got in bootloop flash your extracted stock boot.img with same command in fastboot fastboot flash boot boot.img and you're good to go.

Credits: @shimp208 and @topjohnwu