Looking at entries in Cambridge online, there are these:
- the courage or confidence necessary to do something difficult, unpleasant, or rude:
- the rudeness to do something that you know will upset other people:
In terms of meaning, nerve and 神経 are rather similar. 神経 is used for daring to do something rude. どういう神経・どんな神経（してる） is more or less equivalent to what a nerve. Rather than 'courage'(勇気) or 'confidence'(自信), it is generally called 厚かましさ.
In terms of translation, my impression is that you need to see it as 'what a nerve' in some way even for 'having the nerve'. For example (from the link above),
She's late for work every day, but she still has the nerve to lecture me about punctuality.
彼女は毎日遅刻してるのに、自分に時間を守るように言ってくるのはどういう神経をしてるのか (Literally 'what kind of nerve does she have to lecture me about punctuality')
So, in most cases, that sense of 神経 is used in the form of どんな神経 although there are phrases like 神経が太い/図太い神経をしている etc.