I lack the time right now to look into the game.
Generally speaking there are three approaches to 3d.
1) All the classic 2d era stuff (isometric, mode7 a like and what have you). The DS has some rudimentary 3d hardware but not all things which look 3d use it, also and not all things which look 2d use the 2d stuff exclusively -- new super mario brothers is 3d, the first castlevania notably used 3d in the backgrounds in several rooms and pokemon is 3d for the most part.
2) The official format. This is NSBMD with textures either included in there or separately as NSBTX (do note not everything is a texture and the model colour options do quite well for some things) and animations as NSBCA. Most of the time they are compressed but with standard stuff, most of the time they have those extensions somewhere in the name but not all the time as I have seen some other things in some other games.
Various tools, most of them less than what you might have seen on the 3ds or indeed most other systems
nsbmdtool is the basic thing but fails in some way on most things, newer stuff especially. You might find something better suited for use with pokemon somewhere. Equally it will usually tell you what it got confused by so you can edit the file manually to try to dodge it if you are good enough.
https://filetrip.net/nds-downloads/utilities/download-nsbmd-tool-1-0-f28230.html
Texture wise you have a few more options, some indeed you can even persuade a conventional 2d tile viewer to display..
Tinke is what most would use here
https://github.com/pleonex/tinke/releases
http://gbatemp.net/threads/mkds-course-modifier.299444/ has some things, it is geared towards mario kart DS but it does do more.
Here is a pretty good description of the format
http://llref.emutalk.net/docs/?file=xml/bmd0.xml
You might also like to poke around
https://github.com/Dirbaio/NSMB-Editor/tree/master/NSMBe4
Likewise if anything else is open source around here then it might also be worth a look.
3) Something custom but still close to the hardware.
Hope you know 3d maths and general concepts, here is the hardware
http://problemkaputt.de/gbatek.htm#ds3dvideo
A handful of these have been looked at, most notably Mario 64 and metroid prime
https://filetrip.net/nds-downloads/utilities/download-dsgraph-1-0-f29517.html
http://kuribo64.net/board/forum.php?id=32
You are not going to have an opengl type ripper like some things, though no$gba debug is free these days and has some fairly advanced 3d manipulation and viewing options. As with most play driven stuff you can always cheat and change file names to showcase end bosses/late game stuff right at the start if you want. Desmume has something in the menu but it was a placeholder last I checked (was a while ago though).
All this is geared towards viewing and editing to be put back into the game, if you want to rip more than textures to put into your own game you are going to have to do it yourself. If you want something custom to go back in then some do fiddle with the leaked SDK tools for it but I am not going to help with that one, other than to say good luck finding the ancient version of 3ds max that you will need if you want to head down this path. Others try with MKDS course modifier to convert, it is not my favourite thing to do though.