To unlock the "Refrainer" trophy in "The Bridge" you must complete the second level of Chapter II, "The Precipice", without rotating at all with LT or RT.
Before you start the level make sure you don't have Tilt Controls active -- check the game's menu. If you have Tilt Controls active the game may register an attempt at rotation even if you try and keep the controller still. Otherwise you just need to make sure your fingers are nowhere near the back triggers.
To get the key and get back to the door without rotating the level, you need to use the force of the Vortex's closing animation to launch you to the right of it to get the key, and then back to the left of it for the door. The Vortex opens and then makes five tiny pulses before closing when you first approach it. You need to stand nearby and walk into the Vortex just as the fifth pulse is starting to fling you out the other side to the key. On the way back, the Vortex will only pulse four times before closing so you need to walk into it just as the fourth pulse is starting to again fling you back to the door at the start of the level. It may take a few tries, make sure to rewind to perfect it if you need to.
Note: If you finish the level without unlocking the trophy because you moved a trigger, make sure to quit out of the game entirely before your next attempt. I had problems unlocking the trophy even after a successful attempt but this was resolved when I quit out of the game completely before my next attempt.