So I'm trying to stat out the bite attack of a creature that clamps down on a target, hangs on, and shakes back and forth furiously. To picture what I'm talking about, think of a guard dog biting onto a thief's leg and then shaking its head back and forth to cause further damage. In other words, the attack causes damage both when the animal bites down, and then more damage with each round the beast is able to stay clamped down and thrash about.

What weapon qualities are needed to represent this? I'm thinking Ensnare for the ability to hold onto a foe for more than one round, but then for the shaking... Is that a separate Brawl attack? Or should the attack simply have a level or two of Vicious to represent that particular action?

What you describe as the shaking afterwards sounds kind of like a Burn effect to me. The initial attack is already made, and this is additional damage that happens on the next round and for however many rounds afterwards, as the “guard dog” continues to violently shake his target.

This suggestions is a bit more D20 but....

Perhaps the bite would be the initial damage. And with a number of advantage or triumph, the creature clamps on. While the creature is clamped, it can deal damage until the defender can pry the creature off with an opposed brawl check.

Or if we want to simplify it further.

Initial bite damage as normal, 3 advantage or a Triumph, may deal additional damage equal to ranks in athletics (or Brawl, or Brawn).

Remember that a round could be up to a minute long. It's easy enough to just say that is part of the base damage.

"The beast latches on and begins thrashing back and forth, it's teeth sawing into you. You take X damage."

Shark teeth are the type you need to look out for. A dog or big cat style of jaw may cause some additional tearing, but a sharks teeth are designed to saw through it's prey by thrashing back and forth. Just something to remember when you describe the creature to the players. =)

I'd roll initial damage and have a requirement of 2 or so advantages needed for the beast to latch on (same as activating the special effects on weapons). I'd go with bradknowles' suggestion for burn damage but with some variation. The damage continues to occur as long as the beast is latched on. The target can spend an action trying to shake the animal off (resisted check for athletic probably?), they can shoot the animal with a significant bonus to hit (Perhaps use "engaged" rules which only really applies to the target, since the animal is engaged in latching on for its turns, or perhaps give them boost die), or they can engage in other actions at a significant penalty (Raising the difficulty, putting in a setback die, or perhaps both!). Maybe remove their ability to take an action AND a maneuver each turn to simulate the fact of how difficult it's going to be for them to move while dragging a bulldog with them.

Thanks for the ideas, y'all. The long duration of rounds was one of the things throwing me for a loop; I agree with Ahrimon that it might be enough to describe a beast latching on and thrashing narratively, but assume it lets go before the minute or so of the round is up. I'll have to do some research on animals that attack this way — how long are they known to hold on for?

But the suggestions for a custom critter that can latch on and never let go sounds good, too. I'm still tempted to call it Ensnare (possibly plus Burn, and perhaps requiring some Advantage to activate), since that's what Ensnare is tailor made to do in my reading.