Quoted from pinball_keefer:
The fastest I ever did it by hand when writing it was right around 23 seconds. In my opinion, to get 13, the ring magnet would probably have to be broken. What would happen is the ball would come down the wireform while the opening display effect is still running, you make the 4 shots pretty quick, then shoot the magnet (which doesn't engage) and continue through the back where the ring gets killed instantly. That's actually technically a bug (should require a 2nd hit), but that's what would happen.
Watch this video from ~8:40 on. The last shot to the ring hangs in the magnet and a second ball is kicked out. It will NORMALLY auto-fire and you have to wait for it to make it's way back down. But if you're quick, you can soft plunge and get it on your right flipper much faster.
If you watch from 8:07 on you can actually see him combo the shots the same way I did, except that he blows the Gandalf shot. The ball rolls down the wire-frame, shot to Legolas, shot to Aragon and then it SHOULD have been a shot to Gandalf. Ideally, I suppose, you bounce pass off the Gandalf shot, make the Merry shot. Catch, shoot the ring. I'd be willing to be that the shots could all be made in less than 10 seconds, but maybe I'm being overly optimistic.
It's a lot like the Port Royal/Tortuga multi-ball in PoTC. You put a ball into the spinning disk and the game kicks out another with the intention of auto-firing it, which sends it to the top. If you're quick, however, you soft-plunge it before the auto-fire and can immediately take a shot from your right flipper without having to waste time waiting for it to make its way back down and/or get control. It increases your chances of putting 3 balls in there before the timer runs out dramatically.