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Orochi loses its need to be appeased after being hit by liquid shadow, so the goal is: Feed shadows and riders to make a beefy orochi then hit it with liquid shadow to get a massive vampiric attacker.
The three beguiles should be saved for dangerous enemies. Hit them with beguile then promptly feed them to the nearest orochi. Opponent is short 1 monster, and you have a bigger nastier orochi. Win, win for you.
Try to feed the shadows to the orochi before chowing down on the gnome riders.
Timing on summoning orochi is probably the most critical thing to master. Be sure you either have a liquid shadow on hand, or have enough creatures available to keep the orochi happy until you can find one.
Remember, orochi can eat each other too. While this isn't usually a great idea, it can help in a pinch.
Possible variant: Swap shadows with devourers.