Getting hit in this Secret Mission is not an option as that will greatly reduce and might even reset your Style Rank.
On the first playthrough of the game, doing this mission is almost impossible to pull off. To make things easier, get Hold first. Simply Hold the enemy (preferably a Scarecrow) and stay in a corner of the room while performing Taunts. It will eventually die so go and grab yourself another one. Snatch is not considered an "attack".
Use either Trickster or Royalguard. Having Enemy Step also helps.
Keep dodging and toying with the enemy using the Style's moves and Enemy Step. This might take a while though.