I am in front of her and tried for a several time now. But no matter how I choose the softest choice of each sentence I said to her, I can only chose "I have to kill you (similar words)" to her in the end and trigger the golden rule. There is no other choices in the end for me to choose. Is it because of bug, or I haven‘t done something?

For anyone else in the same position-- I wanted to post that able to get the achievement in a different way *without* reverting to a prior save-- if you threaten Naevia with the golden bow (I don't recall which conversation option it is), you can use its power as a talking point and resolve the encounter peacefully by re-golding Galatea.

that didn't work for me - she was not willing to talk anymore

Did you by any chance have the key to the chest already? You can get it in the pub in a chest. This way, it is impossible to get it from Naevia.

uh, you mean key to Decius's chest? No I haven't got it. Right now I just stuck in front of Naevia and trigger the golden rule again and again... sos

Then..
I had the problem, when I had the key and even used it. For, that palace thingy is for the key.

So sorry, this way, I don't see any reason why. I had the problem, when I had the key already

I'm on my first playthrough: does this mean the achievement for Silver Tongue is now impossible to get since I've found the key to the chest before encountering Naevia?

It is a problem, as you cannot solve that with Naevia, so must go back to the previor save. From that on, you can 'work' your way through and in the end achieve silver tongue. It is just .. you have to go back to the point, before you take that key and use it. So that you can get the key from Naevia in the palace.