The most common modern use. It appears with a negative predicate such as ない, ぬ, ません, or a negative-feeling expression, emphasizing that there is no change, progress, effect, concern, etc.
The rain shows no sign of stopping at all.
completely; absolutely; totally
An emphatic degree adverb meaning fully or absolutely. In modern Japanese it often occurs with predicates that are positive in form but express being unaffected, unconcerned, or acceptable, such as 平気だ.
earnestly; intently; single-mindedly
Rare and old-fashioned as an adverb meaning to do something single-mindedly or intently; modern Japanese would more often use ひたすら, 一心に, or 熱心に.
説明を聞いても、一向に分からなかった。
Even after hearing the explanation, I did not understand it at all.
Even when criticized, he looked completely unbothered.
In older writing, 一向に念仏を唱える can mean 'to chant prayers single-mindedly.'
No matter how much he practices, his skill shows no improvement at all.
Even after receiving harsh criticism, she was completely unfazed.
He doesn't care at all about what others think of him.
It's totally fine even if you're a bit late.
まったく is a broad emphatic adverb meaning 'completely' or 'not at all', while 一向に is narrower and mainly tied to lack of change or effect in negative sentences.
ひたすら is the natural modern word for doing something single-mindedly, corresponding to the rare, old-fashioned 'earnestly' sense of 一向に.
少しも pairs with a negative to mean 'not even a little', much like 一向に, but 少しも is more neutral in register and lacks the nuance of 'no progress at all'.
さっぱり is a colloquial way to say 'not at all' (as in さっぱり分からない), whereas 一向に is somewhat more formal and often used in writing.
一向 is written with 一 'one' and 向 'direction, facing,' plus the adverbial particle に. The spelling is conventionally associated with the idea of being wholly in one direction or degree; the detailed historical development of each sense is not specified.