As far as I know Tiamat being a dragon is more of a popculture thing than mythological. They're not exactly Dragons but beings that fit the same niche "Dragons" just seem to make better boss monsters than a giant whale or turtle, just because they're easier to make meanacing.
Actually, her portrayal as a Dragon is a fault of Christianity. They first started calling her the Leviathan, and then they started alternatively swapping the use of "Leviathan" and "Dragon" in references to her during the book of Revelations. Yes, Tiamat was in the Christian bible, although never referred to by name. You need to have read both the bible and also Babylonian texts to catch the fact that every single reference to "Leviathan" in the bible actually describes a thing that Tiamat did in the Enuma Elis in the old-testament parts, and then in the later new testament the terms "Leviathan" or "Dragon" are always used in very close association with a figure referred to as "the whore of Babylon," thus further cementing in the close association between this "Leviathan" and Babylon.
The whales and turtles thing is relevant to note however, because there is another pop-culture dragon who actually was portrayed as a whale or a turtle. Those are the frequent pre-pop culture representations of Bahamut. I've seen him represented as either a large fish or a turtle in illustrations of the Hindu version of their representations of the world, which are supposedly that the world is a disk set atop the backs of giant elephants, and those giant elephants in turn are standing on the back of Bahamut who is some form of sea creature.
We all know how Bahamut is depicted in modern-day representations. Anyone who's ever played the Final Fantasy series has seen him as the ultimate dragon summon, and those who have played D&D know him as a draconic god and leader of the metallic dragons.
(Funny thing though. I've mentioned Bahamut to actual practitioners of the Hindu faith. You're as likely to find a Hindu person who realizes Bahamut is a figure from their own religion as you are to find a Christian who knows Azazel is from Christian Angelology, much less explain who Azazel actually is in the first place. (Azazel is the angel of death, FYI. In modern day, he is called by his alternative title, the Grim Reaper, and is portrayed as a skeleton instead of his original portrayal as a black-winged angel. In several ways, he has experienced a very similar transformation to the one Bahamut went through. EDIT: And, yes, it's a sure thing that Azazel and The Grim Reaper are one and the same. It's actually possible to track the artworks portraying Azazel starting to wear a dark cloak and holding a scythe in the early parts of the Bubonic plague, become surrounded by skeletons in later works, and then becoming the skeleton himself with the same paraphernalia by the end of the plague era.))