Bats are not birds. Just as fish are not (birds).

Literal

Bat [topic-は] bird is-not. That [topic-が] fish [copula-で] that-way-is [and-と] same is.

A logically dense sentence with an awkward phrasing — hard to parse even for natives. The structure seems to be saying 'bats are not birds, just as fish are not (birds)'. The 'そうでない' refers back to the predicate 'is not a bird'. The phrasing is stiff and reads like a translation exercise or a logical proof — low in naturalness.