Is that a baby Zoidberg? hehe
Nah, Cthulhu.
Looking at the title I was expecting some kind of cthulhu a la japanese salary man, due to "Tamaguchi" bein a Japanese surname. But I guess you meant Tamagotchi.
Design wise, I guess the idea is nice, but shouldn't cthulhu be smaller?
I mean, right now it is sleeping sideways, and almost fills the whole screen. That meaning it wouldnt be able to stand.
Pixel art wise, I guess you wanted to keep the tamagotchi feeling for the creature, but the GUI (if it can be called like that) could use a lot more work.
It looks flat and well, I guess it could be more detailed (AA'd, usage of a more interesting palette, adding highlights etc etc).
As for the c64 palettes, here is a link to a post ptoing made with information regarding that.
http://www.wayofthepixel.net/pixelation/index.php?topic=1618.msg19540#msg19540