Couldn't you also say "skilpadder lever i vannet"? Is the "nede" really necessary here?
If you drop 'nede' it would mean that the turtles might as well swim on the surface. When adding 'nede' you indicate that they are mostly deeper down in the water.
Don't you think that translation "turtles live under the water" would be also a correct one? I know that it is not direct, but I guess that would keep the same meaning.
I'm unsure, it could lead people to believe that "nede" means "under", rather than "down".