This is an achievement that the whole world is watching.
Tips
usage
举世 is bookish and almost always functions as an adverbial premodifier in fixed four-character patterns: 举世闻名 (world-famous), 举世瞩目 (world-watched), 举世无双 (without equal in the world), 举世罕见 (rarely seen anywhere in the world). Don't try it as a free-standing word.
memory
Literally "raise / lift the world" — but 举 here means "the whole / all" (as in 举国 "the whole country"). Mnemonic: "hoist up the entire world" → "the world over."