She actually dared to go to such a faraway place by herself.
Tips
usage
竟敢 expresses shock and indignation that someone had the nerve to do something. It is stronger than just 敢 (gǎn, to dare). It almost always implies disapproval or surprise.
register
竟敢 is common in both spoken and written Chinese, but especially in dramatic or confrontational contexts. You'll hear it frequently in TV dramas and arguments.