There is objectivity in epistemology, in matters of what is true or false.
There is objectivity in ethics, in matters of what is right or wrong.
There is objectivity in aesthetics, in matters of what is beautiful or ugly.
The fact that these things are difficult to achieve and that we don't always know if and when we have achieved objective truth or rightness or beauty should not be confused with the fact that they don't exist. That would be confusing the subjective with the objective.