得意扬扬 often carries a mildly negative connotation - it implies someone is overly proud or showing off. The variant 得意洋洋 (déyìyángyáng) uses 洋 instead of 扬 and is equally common.
grammar
Used as an adverbial with 地: 得意扬扬地 + verb. Also used as a predicate: 他很得意扬扬 (less common, 他得意扬扬的 is more natural).