Once(upon )a time , there was a king firing (at/to )an animal, but he failed.

I think both "at" and "to" are ok, am I right?
I don't think 'to' is correct : 'at' is definitely better. I think 'on' would be acceptable, but not 'to'.
If the context is shooting, only 'at' is correct here. One never says 'firing to', though one can say 'firing towards', or 'firing into', as in--

'He was firing towards the sound coming from the bush.'
'He was firing into the crowd of bystanders.'

'He was firing over their heads, as a warning.'
'They were firing upon the advancing troops.'