Your predator will be throwing offensive combinations at you, while your prey launches defenses. To succeed, you need to find the link in their combination you can best attack and go for it. Every time you fight each side loses a couple of blood. If everybody spent 20 bringing out vampires, by the time you've lost 10 against your predator and 10 against your prey, you're down to 0 blood - and out of commission. Your opponents are still operational, at 10 each.
Similar issues apply to other resources, like untapped vampires.
Because Jyhad operations demand combinations, you can always be clever by picking on just one link of your opponent's combinations. Some of the classic resources, and ways to attack them. Vampires with a particular skill - Combat is the way to go. Clan hosers, Golconda and Hostile takeover can do nicely too. If he needs skill cards, use your Sudden Reversals for them.