As with all team issues (even though your friend’s pokémon is technically not on your team), it’s important to communicate in order to determine the actual cause of negative behavior. In this case, your friend should be the one to take his nidorino (I believe? I apologize if it actually is a nidorina, as mentioned in the first line.) aside and determine the root cause of his behavior, then work with you in order to find a workable solution. There’s not much you can do on your own, as it sounds like your mimikyu is well-behaved as it is, which means the issue lies with your friend’s nidorino alone.
However, I can offer a bit of insight as to what may be causing the rift between your mimikyu and your friend’s nidorino. You see, as a ghost/fairy-type, mimikyu sit at a rather unique crossroads. Both types are notorious for their mischievousness, and as such, even other pokémon tend to be wary about them. It doesn’t help that mimikyu are often either shy or the vindictive sort of envious, so it’s honestly no wonder that your friend’s nidorino is especially cautious when he sees your mimikyu.
For this reason, it may be prudent for your friend to teach his nidorino that not all mimikyu aim to trick humans or attack them out of envy. Consider proposing exposure therapy, wherein you introduce both pokémon in a comfortable setting for short periods at a time and work your way up to a point where your friend’s nidorino can safely exist in a room with your mimikyu without attacking her. Either way, the process would be gradual, but it’s up to your friend to work with his pokémon.
Best of luck to the both of you!
The Pokédex According to Bill 