Translation:The hat is as beautiful as the dress.
Well actually, the contraction "hat's" of "hat is" is perfectly acceptable in written English. It depends upon whether you are talking about formal written English or not. Either way, it's allowed, as much as "it's" is allowed, but it's kind of frowned upon as long as its writing is not in a professional document.
Saying "the hat is" is certainly clearer, however.