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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?
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I don't think 'to' is correct : 'at' is definitely better. I think 'on' would be acceptable, but not 'to'.
Waïti.
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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.'

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