I think Rosenstein is the only one that can fire him. It wouldn’t look good if Trump did so. But Trump can certainly expose Mueller and his liberal army for what they are.
I don’t think the President can fire anybody in the DOJ except the AG and Deputy AG. It’s not a situation unique to Mueller.
https://www.justice.gov/jmd/organization-mission-and-functions-manual-attorney-general
...The major functions of the DAG are to:
Exercise all the power and authority of the Attorney General unless any such power or authority is required by law to be exercised by the Attorney General personally...
...Be responsible for all DOJ attorney personnel matters, including final action in matters pertaining to the employment, separation, and discipline...
Comey was not fired through the chain of command. Trump fired him directly.