How does a Muslim atone for not performing Fajr prayer despite waking up at the time of the Adhan?

All praise is due to Allah, who has blessed you with awakening after heedlessness. So, praise Him and be grateful to Him, and expiate for that with repentance and regret. Refer to Fatwa No. 32521 to learn about the conditions for accepted repentance and the signs of its acceptance. And you should admonish yourself for how you hear the call of Allah and do not heed it. As for making up the missed prayers, its ruling has been previously explained in Fatwa No. 144683 and its related rulings. For further benefit, refer to Fatawa Nos. 119346 and 92159.