Nah this battle can be fought in the same way than other traditional battles. The only difference is that this enemy mimics all your stats and elemental defence and will always perform the same action as your last, except if these defenses and actions involves HP healing. For example, if you got 2 vital rings equipped, it raises your defense, so when fighting this monster he will have much higher defense. However, if you got 4 regen rings equipped, which restores your HP every turn, the mime will not mimic that protection. In other words, he won't get any HP restored every turn. If you use PSY or CURE, both magics that can restore your HP, he'll perform no action. Psy absorbs HP from enemies unless they're immune to dark magic (like the mime himself) and Cure obviously restores your HP.
This battle is actually pretty easy. However, if your defense is extremly high, the battle will take A LOOONNG while. If your attack is too high, you'll receive considerable amount of damage from the enemy. I think I will actually show two screenshots of this enemy battle to demonstrate.
First one will be at my current LV. Secondly will be at extremly high LV
