*I do not take credit for this solution, This was posted on Playstation trophies org. I added the link below as Citation. There was no author listed on the site to credit for this solution.
Edit: i believe the author to be dcollins22http://www.playstationtrophies.org/game/puppeteer/trophy/691...
This trophy can be obtained in Act II, Curtain II whilst fighting the Kappageru which is a mini boss you will face roughly half way through the level. In order to unlock this trophy you must not land on either platform to the left or right of the screen. Remain in the air by continually cutting the purple mesh by spamming Square . Unlike some other materials that can be cut, the purple mesh will not disappear once you cut it. The boss only has a few attacks which can easily be dodged by moving back and forth from left to right on the screen. Throw bombs at her head by pressing O . It takes a total of 6 bombs to defeat her.
- Try and stay as high on the mesh as you can as at certain points of the fight the purple mesh disappears for a few seconds and you are left in the air with nothing to cut.
- If you accidentally land on one of the platforms, kill yourself by jumping towards the Kappagaeru and lose all 3 of your heads. You will then restart at the beginning of the boss fight as opposed to having to replay the entire level over.