As far as I know, every federal official can be impeached. The FRB legislation also specifically mentions removal by the President “for cause”, which seems unusual to me at first glance.
The Fed chair is not an executive branch position so the president cannot fire Yellen at will. In a 1935 Supreme Court decision, Humphrey's Executor v. United States (295 U.S. 602), the court ruled that an officer who is not in an executive branch position may be removed only with procedures consistent with statutory conditions enacted by Congress. They cannot be removed solely for political reasons. So if Yellen can indeed be removed "for cause" then Congress needs to identify what that "cause" is and Yellen has to violate it. Did she?