Spiraling Claw is Kat's special attack in the default style. You can perform it by pressing
and with the red meter under the health bar full, which auto-locks onto enemies and sees Kat spinning repeatedly to create a circular motion which kills most enemies it collides with. To earn this trophy, you must defeat ten enemies with a single use of this move (in other words, you can't kill 2 then use the move again and kill 8 - it must be 10 with one press).
I found the best chance to earn this is during the many story missions involving military guards, who use guns and wear circular hats. For example, on "Like a Radio" you'll get the opportunity to take on dozens of guards and can easily earn this. Same with "Wandering Heart" where you face waves of guards before a boss fight spawns. Just make sure you aim for enemies away from cover, as you can end up drilling into a wall and needing to build your meter up again. Don't forget to check for Red cubes which can instantly fill your special meter.