There are multiple approaches they could have used here.
The most basic would have been a flag. That is to say a small area you put to 1 or 0 depending upon whether it is edit locked.
This sort of thing is fig leaf security but it is common enough in things that don't matter or would be complicated to handle otherwise.
Easy enough to try this. Make a level (does not matter what). Save it. Grab the save. Go back, password the level (maybe even remake from scratch if it was simple enough). Grab the save and compare. Any differences then being what you want to look at.
Sorting this gets harder. You might have to learn the save checksum/hash routine and fix that, or stop the checksum from mattering ("compare checksum to stored checksum if equal then proceed to works outcome if not equal then proceed to invalid save" can so easily be tweaked to always take the valid checksum path, with the added bonus that the game will probably fix it for you next time it saves and can be exported back to a unmodified game). Of course if the password itself it not going to be a dissimilar concept (check if good, if not then... yeah) then you can possibly attack the password aspect itself -- find where the save is loaded into RAM to be operated upon and then you will know where the password part is stored, easy enough to nerf it that way.
If it is a basic flag then you might find where the save lands in memory and some time between the copy and the final load you might be able to disable the flag. Timing of things can be tricky here but you might also be able to do it manually if you play around a bit and find out if it does not do anything with read only flags before.
Passworded however does not mean encrypted (data unreadable, indeed that the game can be played but not edited would speak to a lack of encryption worth much). To this end some might find the data of the level (be it in RAM or in save) and export that around to create a "new" level.
You might even get lucky and find the password stored in the save in something you can read or maybe bypass on the PC side of things. As before you are going to want many saves, I don't know if you set passwords or they are generated. If they are set then you are going to want to make save, set password as AAAA or whatever and then AAAB and then AAAC... to get an idea of where the password is stored in the save. In an ideal world it will be in some kind of plaintext, if the devs were slightly tricky they might do some maths on it to change things and make that harder and in big boy security they would have done some kind of salted hash (storing passwords is bad for what are hopefully obvious reasons, storing a unique hash of the password and an extra random piece of data such that the game does not know the password but can be mathematically sure of the right one being entered is good).
If it is a hash then you might get to play rainbow tables instead. AAAA through ZZZZ is a lot to write out by hand but trivial for a modern computer, more characters (maybe lower case and numbers and punctuation) and longer passwords make things harder but the chances of a DS game having high end takes here are slim. At this point you look up the hash and find the/a matching password.
Other than the cheat based flag or plaintext stored password I don't know if I would suggest it for a first project as most of that will see you run into at least light assembly work. If however it is going to be the thing that gives the project some sticking power for you then go for it.
A minor note on wear levelling. Saves for things with valuable saves will possibly have two slots for it and alternate between the two to both stop one section from being written all the time and also providing something of a "lost progress since last save" backup but better a couple of hours than a couple of weeks of work. To this end the naive compare two files of a hex editor might not work. Find what sections constitute these sections/slots and rip those out to compare to relevant parts, or save twice (or more if it is weird and has many slots) such that it ends up back at the main slot.
