Once you enter the room the Oracle is hanging in, drag out the 2 statues near the entrance. drop one down to the lower level, and then drop the other one down on top of it so they're stacked up.
Once they're stacked, drag them to the left of the door that says only the Oracle can open right next to the raised platform. Jump on top of the doorway, then jump up again to the raised platform. Jump on the pillars, then jump over to the vines. This is when the clock will start ticking.
Jumping on the vines is much faster than simply moving. Also jumping across the balance beams is faster if you can land the jump. You are given 60 seconds to complete the obstacle course to catch her, so you're not going to want to stall for any reason. If you fall, it restarts you at the beginning vines with 60 seconds again, so you don't have to worry about having to climb all the way up again.
Other than that, just complete the obstacle course with 10 or more seconds left on the clock and this Trophy is yours