Option A: 'Regardless' means 'without any consideration of'.
Option B: 'Regard' means 'consider or think of in a specified way'.
Option C: 'Regarding' means 'in respect of, concerning'.
Option D: 'Regards' means 'best wishes'.
From these words, 'regardless' is the most appropriate word, as it completes the sentence in meaning: She decided to stick to her decision no matter what the consequences may be.
Hence option A is correct.
The other words do not complete the sentence in meaning, hence B, C, D are incorrect.