The first - and already very big - challenge is to detect in real time whether a bubble is developing. Asset prices are inherently forward looking and it is very difficult to assess ex ante whether the expectations underlying an ascending or descending trend are realistic or are just validating themselves.
In this respect, the central bank typically has no better knowledge about future fundamentals than the market itself. This does not mean that a central bank is left all by itself in the face of major asset price movements.