What is the limit of plaintext required to break the Vigenère encryption?
For chosen plaintext and a classic Vigenère cipher, you need only as many characters of plaintext as the length of the key to completely recover the key. It's a trivial reversal. (If the cipher uses 26 scrambled alphabets, it will take more.) if you don't know the length of the key, you will spot the repeating sequence after the second repeat.

For an unknown ciphertext, that's when it gets interesting. You need enough repeats of the keylength to measure the index of coincidence. The Friedman test provides a way to estimate the amount of ciphertext.