Use logic, really. There are a two main things that can be figured out just by looking at the scrolls.
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1. The "Toggle 4+5" orb has to be the last orb because it is the only one without a "Close". So you have to end up with Gates 4 and 5 closed with the rest open. (Including this one, six of the orbs affect those two gates. Five are "Close" or "Toggle".)
2. The "Toggle 3, Open 8, Close 7" and the "Close 8" are the only two orbs that affect gate 8. Therefore, you will never need to use "Close 8."
After this, it is probably easiest to write something down on paper (That is what I did). However, trial and error can work - you'll see why when you solve it.
There is also a post on the forum somewhere about it. It asked how few orbs you needed for the quickest solution. I think it's five, but there is a longer way which is easier to figure this out.
Hope this helps.....
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Slashing, whirling, diving, twirling,
Snapping, turning, rising, swirling,
Screeching, flipping, gliding, sliding,
The red hawk's dance of death.
.....the king of the skies.....