There is a
tutorial for upgrading 4.1-8.1 to 9.0-9.2 in this board.
I don't mind repeating it again though.
Part 1 - rxTools installation
1) Download the latest rxTools 3.0 nightly.
2) Copy "rxTools" folder to SD root.
3) Run /Tools/cdn_firm.py, it will download a "firm" directory.
4) Copy the "firm" directory into your SD://rxTools directory.
5) Download slot0x25keyX.bin from the Internet and copy it to SD root.
6) Copy /mset/rxinstaller.nds to your DS flashcart, run it, and choose 4.X. If you don't have a DS flashcart, use dukesrg URL to boot rxTools instead.
Part 2 - FBI injection
1) Enter Recovery Mode to delete all auto-downloaded updates. If you don't do this, FBI injection may misjudge the TMD version to make the injection unsuccessful.
2) Copy /Tool/fbi_injection/eur/2050 all files to SD root.
3) Enter System Setting -> DS profile (we called this step "414") or use dukesrg URL to boot rxTools.
4) After booting to rxTools, go to Advanced -> FBI injection and follow the instruction to inject FBI into your SysNAND.
Part 3 - Upgrade 4.5.0-9E to 9.2.0-20E
1) Download 9.2.0-20E full pack from the ISO site.
2) Extract all the files to SD://updates.
3) Download Sysupdater 0.4.1 and extract it to SD.
4) Use 414 or URL to boot rxTools. Hold L to enter rxTools menu.
5) Go to Advanced -> Pasta mode.
6) Use Health & Care applet (which is actually the FBI you have injected) to install Sysupdater 0.4.1 CIA.
7) Use Sysupdater to install 9.2.0-20E full pack.