Unrepentantly is the adverb: doing something, or being something, without any sign of being sorry about it. "He unrepentantly repeated the joke that got him in trouble." It tells you how the action was done — openly, with no apology in it, and often with the person knowing perfectly well that others disapprove. Like the adjective, it splits two ways. In serious writing it is disapproving: "the company unrepentantly carried on". In lighter writing it goes in front of a description and means "and cheerfully so": unrepentantly old-fashioned, unrepentantly sentimental, unrepentantly loud. "The restaurant is unrepentantly old-fashioned" is a compliment — it knows the fashion has moved on and it does not care. That second use is friendly and quite common in reviews. It is a written word. Speaking, you would say "without saying sorry", "and he wasn't sorry at all", "and proud of it". A note on shape: it is long, four beats plus, so writers usually give it room rather than stacking it with other long words.

毫無悔意地、死不認錯地；也常見於輕鬆語氣，如 unrepentantly old-fashioned（就是老派，而且完全不打算改）。