How would one crack a weak but unknown encryption protocol?
It depends on what information you have. If all you have is that one ciphertext and no way of acquiring more, there's not much you can do.

If you have multiple ciphertexts, you can try to observe any patterns in them. If you have the corresponding plaintexts, you can really start to make some useful observations. If you have some plaintext, ciphertext pairs, you can try to find patterns in the data.

An even stronger attack would having access to the encryption oracle. That is, being able to encrypt plaintexts of your choosing. Here you could try special encryption strings to see if they leak any information about the algorithm. You can try things like "a", "aaaaaaa", or string of null bytes and see what information you can extract about the algorithm.

If the encryption algorithm is insecure, your goal should be to figure out what the algorithm does. Once you know how the algorithm works, you can presumably figure out a way to break ciphertexts or get the key.