Not sure what you mean.  There are 9 trials possible in each form of Chimera. 

Now there are only 2 trials of viper form in 1 game, how to complete four of them?

There are 2 rounds of Viper.  Each  form of Chimera has 9 available trials that can be completed.

Now I fought 1 quest until the end, but it didn't count. With (only) 2 rounds of Viper.  

The quest requires FOUR Viper form trials - so my question is: do I have to sacrifice another "Hard Chimera" round to get the 4 requested?

You have to do 4 or more trials in one run on Hard or Higher, in one run. 

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These are the 9 trials available during the Viper form.  You need to complete 4 of them in one run.

Ok, now I understand, thanks a lot!

No problemo.