You have to kill the Sin Scissors with one blow. One way to do this is to use the Shotgun at range to stun it: The blast should hit it in the scissors and only knock it off balance, and not damage it. When it's stunned, run in to point-blank range and blast it again in the face. This should do it. Devil Trigger might help if you can't get it the first time around.
If you can't master this technique, another one to try is to wait for it to attack. Jump over the attack or jump back, such that you're stil face-to-face with it, and attack it with your sword from far enough away that you just hit the scissor, not the Sin's face. This should cause it to stagger and put you a step closer to it. Activate Devil Trigger and step forward while aiming your shotgun. Blast it as it's recovering. If your timing is right, you will fill its face full of buckshot just as it tuns its mask towards you.
Because the area you're in drains your health, you will have an issue with surviving multiple attempts at this secret mission. Using Devil Trigger will not only help you kill the thing quickly, but it will halt your health loss. As you wait for the Sin Scissors to drift down into your range, take this time to taunt it to fill your DT gauge. You can fill up to four runes before it even gets close enough to attack, provided you use double-handed taunts. This way you will always have full Devil Trigger for the fight.
- On the DMC HD Collection for xBox 360, you cannot be killed by suffocation damage ie. by simply being underwater. If you do not get hit by the Sin Scissors you may remain underwater indefinately - your health will reach magic pixel but you will not die.
Also, you do not actually have to kill it in one hit, so long as you trigger the instant death condition. - Verified on Ps3 HD collection