Hello, I'll start off with saying, yes I know about 3DNUS and yes it is a better yet potentially more challenging process so here is the alternative. I've seen many people asking about how this is done, and this is by far the simplest process to update your emunand without using the eshop.

Disclaimer - I hold no responsibility if anything here bricks or damages your console. Follow these steps at your own risk. Make sure to only update as far as the gateway site claims to supports your console.




And we're off...

Something not everyone is aware of is that, UNTRIMMED roms are .3ds files that haven't been watered down or shrunken in size. These roms actually contain system update files for the firmware they require to be played. This tutorial let's you use that update, IF you are using an UNTRIMMED rom or a trimmed rom that you KNOW still contains the system update files.

Negatives compared to 3DNUS method:
1. You can only update your emunand as far as the latest rom, not the latest released firmware.
2. These updates are not FULL updates, but rather "tide you over" updates that will give you the necessary functionality to play games requiring that firmware. For example using a rom you can update to 9.2.0-10u but with 3DNUS you can update to 9.2.0-20u. The last 3 characters are the distinguishing factor. (Information provided by DjoeN)
Currently unsure about what gets left out but since they both are provided by Nintendo, it is unlikely that this will cause any longterm damage.

Stuff you need:
1. 3ds, Old 3ds XL, New 3ds, or New 3ds xl at 9.2 sysnand or lower.
2. Red Gateway card with microsd.
3. Untrimmed rom which will be further explained in the procedure below.(Trimmed rom that wasn't trimmed of it's update files will also work if you can find it - Info provided by MattKimura)
4. EMUNAND on your 3ds' internal SD or microsd card. (If you don't have this, you've got bigger problems at the moment. Figure that out first and the revisit this tutorial )

Procedure:

1. Check which firmware is available on which roms HERE. This site won't tell you where to find said roms, so I trust in your intelligence to find THE EXACT UNTRIMMED ROM you wish to use.



2. Scroll to the right and filter descending by firmware.



3. Find the latest 'releasename' with the target firmware for YOUR region. At the time of writing this guide, that is 9.5 for EU and 9.4 elsewhere.

4. Find the EXACT .3ds rom listed under 'releasename' using some good old fashioned interwebz 'know-how'. I say exact because people will release trimmed or watered down versions of the game to save on space, and often the first thing to go is the large system update portion of the rom, aka, what we're looking for.

5. Put the .3ds file on your GATEWAY RED CARD'S microsd, NOT THE INTERNAL ONE.

6. Get into the Gateway Menu but DON'T LAUNCH THE EMUNAND VIA GATEWAY MODE yet.

7. Hold UP on the D-PAD and then enter the emunand via gateway mode while continuing to hold up.

8. When in emunand, hit select, and choose the rom like you normally would from the gateway thingy on the top screen. Here I'm using a rom of super smash to update to 9.2 emunand.



9. LAST WARNING, IF YOU ARE NOT IN EMUNAND AND ARE IN SYSNAND, THIS WILL LIKELY BRICK YOUR CONSOLE SO MAKE SURE YOU ARE IN EMUNAND!!!!!!!!!!!!!

10. Launch the rom and the following popup should show, SPECIFICALLY MENTIONING THE VERSION OF THE FIRMWARE YOU'RE updating too.



11. Please tell me you're in emunand and not sysnand by now, because this is warning #3.

12. Hit A and follow the step to update like you normally would. The System will restart.

13. Relaunch the emunand like you normally do and confirm that you've updated to the desired firmware.

Hope this helps somebody!

 

You should mention that an update from a ROM is not a FULL system update, certain parts will not be updated, you know when a system is updated from a rom, the last digits mostly are different then the OFW
9.2.0-20U updated with a rom to 9.5 will be 9.5.0-20U
9.2.0-20U update with System update to 9.5 will be 9.5.0-22U (or 9.5.0-23U) (Now you need to use 3DNUS for that)

Your screenshot example is 9.2.0-10U, indicating you are updating a 4.3.0-10U / 4.4.0-10U / 4.5.0-10U System with a rom to 9.2.0-10U instead of 9.2.0-20U

While using 3DNUS to update your emunand is equal to a full system update
Maybe you should aswell write a guide on how to do it with 3DNUS on this thread so people can see both on the same page and compare and decide for themself on how the will do it.

 

There's two programs you can use for trimming 3DS roms with no problems:

1. CTR (Crappy Tiny Reader)

2. Tokyo Rom Trimmer (Recommended)

I suggest Tokyo Rom Trimmer, it can trim all your roms at once. Just be sure not to trim card 2 games: Pokemon, animal crossing, tomodachi Life.
You can untrim roms with CTR, but there's no need to untrim a rom once trimmed, I can guarantee that.
On CTR, there'a an option to (Super trim), which removes the update from the rom. This is the only way to remove the update from the rom, you can pretend it doesn't exist.
There's absolutely no down sides to trimming roms. Not like DS roms and PSP iso's back in the day.