Welcome to the forum! Having looked at the game quickly on YouTube, I'll be quite happy to help you dump the text. Since the game only uses hiragana and katakana, it shouldn't be too big of a job.
A guide for the NES will usually suffice for the GBC since the principles remain the same. Some games are quite different because of how the graphics work. On the NES, the entire alphabet or kana needs to be loaded into the video RAM in one piece because the NES can't directly access the memory. This isn't the case on the GBC, so in some games only the characters which are necessary are loaded into the VRAM, and this can make finding the text a little more tricky.
Anyway, give me a bit of time and I imagine I'll be able to dump the text and explain how I did it.
EDIT: Okay, here's what I've done so far.
First thing I always do is open the ROM in Tile Molester to see what graphics I can see. It can be a neat shortcut to just look directly at the ROM, if there's no compression. GBC doesn't commonly use compression because the ROMs are so huge. A quick rush through the ROM leads me to a couple of character sets at $442A4 and $452A4 (pressing plus and minus moves byte-by-byte, which is necessary here because it starts at $A4 not $A0). This is a good sign, so I make a table file with Tabular that corresponds to what I see.
So Tabular makes things pretty easy: you can insert Romaji for kana and alphabets with a click of a button. You can mess around with the table file later, but it's a good start. Save it as a .tbl file and open up WindHex32 EX, as this is a hex editor that supports table files. Open the ROM and the table file in the File menu. Now, we don't actually know where the text is, but if we were right about our table file, then we can actually do a search for the first line of dialogue.
The first line includes "omatase" (I'm using Romaji for ease of reading), but WH32EX sucks at searching, so let's open HxD instead, since it's a much more comprehensive hex editor all round. Let's search for the hex instead: open the table file and look for the four hex codes for "omatase". It's 65 7F 70 6E. Ooh, one match: $6C2AB. Let's go there in WH32EX...
Well look at that: looks like we have the actual dialogue.
Let's try changing "omatase" to a word using the English alphabet already in the ROM...
But hold on, it's not as simple as that. You see, there are control codes to say when to go to the next line, when to wait for a button push, and so on. Those are usually kind of easy to get to grips with, but here there's an extra complication. If you look at what's there, you'll notice some weird characters in the middle of the dialogue, so you get things like "haya#ku Masuda-san no # ie ni #kou yo", with the #s being things that really shouldn't be there. This indicates something a little more complex, so I'll have to take a closer look.
Still it's a start, and it should give you some idea of how to do this in the future.
Just give me a little more time, and hopefully it won't be difficult to figure out what's going on with these weird characters.
(I should put a disclaimer that the method I used here is certainly NOT going to work every time - if a game uses compression of either the graphics or the text, you'll need some more advanced skills)