Consider a cipher where the method of encryption is to perform a Vigenere cipher on a plaintext, with the key word being an affine cipher of the letters a,b,c,...,z.
How strong would this cipher be? Would it be possible to crack under a ciphertext only attack?
Yes, it could be broken using a ciphertext only attack given enough ciphertext.
Breaking vigenere ciphertext typically involves brute forcing the length of the key, then running statistical analysis. In this case, we already know the length of the key (26 characters), so we can go right to statistical analysis. With enough ciphertext this would be easy.
Obviously this is assuming knowledge of the plaintext language. In practice, that isn't too strong of an assumption, however.