Gotta say, this problem did get me nervous.
Can confirm it's an emulator-specific problem, not the game itself.
I tested the original game and the hack in both melonDS 0.8.3 and Desmume 0.9.11, and the original and the hack both had the issue in melonDS 0.8.3.
Desmume was the one that had the graphics right.
The images seen above were taken from Desmume 0.9.11 (64bit build).
I tested both the original game and the hack, and both games, as well as both the Invisible Man and Death, show up properly with that build of Desmume.
So glad this wasn't a side effect of the new portraits, what a fucking relief xDEDIT:
Turns out that turning Software Rendered on in the Video Settings of melonDS seems to fix the graphical glitch too.
So the game should run fine on melonDS as well with that option enabled.