Blatantly is how you do a blatant thing: openly, without bothering to hide it, and without looking sorry. He blatantly copied her homework. She blatantly ignored the rule. In careful English it still points a finger — this is bad, and they are not even covering it. In loose talk, especially among younger speakers, it sometimes drifts toward a mere “clearly” or “obviously”: “That’s blatantly not true” can just mean “that’s obviously not true.” Teachers and news writers usually keep the sharper, blaming sense. You will also meet the slightly puffed-up phrase blatantly obvious, which says “obvious” twice; people still say it when they want extra heat.