How to get the serial monitor to only show a specific part of what it outputs?

[Grumpy_Mike]

if (client.available()) {
    char c = client.read();
    Serial.print(c);
  }

Here you are reading bytes from the client. As well as printing them out test to see if they are a CR, if so increment the CR count.
When it gets to the right number ( as found from counting how many lines you have before it finishes ) start saving the variable c in an char array. This is then the data you want.