While this trophy is typically a bit challenging, it can be bypassed (at least, as of right now) by utilizing what the game gives you. By unlocking all ten gallery doors, the Mayor will give you a Magical Tiara that grants you unlimited magic. Couple that with a level three spell like Flamethrower or Storm and you should be able to lock yourself in air and prevent any of the gears from damaging you, ever.
Should you be interested in doing this without a cheat, the goal is to jump over every gear and dual-gear in your way as you escape the hideout. You CAN die and re-start this, but only if you have not hit a gear at all. If you did hit a gear, you will unfortunately have to quit and go back through the boss fights prior to this point. For that reason alone, I'd definitely suggest just using this to get it over with as soon as you can during your first run.
To prove my point, here's a video: