Japan's long-cherished dream of gold in synchronized swimming fell just one step short.
Literal
Japan synchronized-swimming world [possessive-の] long-cherished-wish [copula-である] gold [at-には], another one-step [with-で] not-reaching.
悲願 (ひがん, 'long-cherished dream, earnest wish') is commonly used in sports for goals a nation or team has pursued for years. あと一歩で ('by just one step') conveys near-misses. 届かなかった ('didn't reach') is the negative past of 届く. シンクロ界 ('synchronized swimming world') uses 界 ('world, sphere'). A classic sports-news near-miss sentence.