Byakhee

My take on this set: There are a couple of Byakhee enemies that the players meet throughout Carcosa. Ironically, the one in the Byakhee set is probably the weakest of the bunch. The real star in this set is the Hunted By Byakhees treachery then, which increases the chance for the more dangerous ones to be drawn. This set does its most important work during Phantom of Truth, where it brings up the number of Byakhee related cards to the level needed that they can feel like a constant threat. During Black Stars, it’s more filler and interacts only with its scenario specific Riftseeker enemy.
This is a fine set of cards that is maybe a bit underused by the campaign? Only two scenarios feature these enemies and one of them only does so as an afterthought.

What it does: The Swift Byakhee has below average fight and evade and the basic 1 damage and horror. Only its health of three gives it some staying power. It does have Retaliate, but the low fight value means that is only going to be relevant for investigators that are unprepared for combat.
The Byakhee has Hunter, and in fact does use a special version of the keyword that allows it to move any number of locations to find someone to engage. If they did, they forfeit their attack in that phase, though.

My take: That souped up Hunter ability means one thing to me: This enemy is to be defeated, evasion is not a great option. Luckily, this is not as difficult as the other Byakhees can be. It might take two attacks sometimes, but usually this thing goes down the turn it enters play, never to make use of any of its special Hunter rules.
If you are finding yourself without a combat ready investigator and rely on evasion, this enemy does become a huge problem, though. Attacking it without a weapon (or a weak weapon) risks extra attacks from Retaliate and evasion would eat up a lot of actions over time. Still, i would say this would be your fault for being unprepared…
All things considered, this is the weakest Byakhee in the game so far. The rest of them do all deal a whole lot more damage and/or are much tougher to kill.

Threat level: Low. Can be killed off easy enough to usually not be a problem.

Dealing with it: This sort of enemy is the reason why even evasion focused investigators should have something in their back pocket to deal damage sometimes. To offer two examples, Backstab does a great job of killing this thing in one action for rogues (and Wendy). Acidic Ichor does the same for Seekers.

What it does: The player has to take an agility test that is very hard to pass. For each point they failed by, a card is discarded from the encounter deck. If a Byakhee is found, it is drawn and spawned. If an Omen is found, the player takes a horror.

My take: There are a lot of moving parts here and drawing this card is a bit of a gamble every time as the effect is determined by layered chances. But still, the worst case scenario is having to engage a Byakhee enemy and getting a horror on top. Often, this card will act just as if you had drawn the enemy itself, so it acts as extra copies of any Byakhees already in the deck.
Phantom of Truth has six Byakhees in the deck, Black Stars has four. Not only is this card more likely to draw an enemy during Phantom, but it also has the Agents of Hastur set or its replacement, which do in my opinion have the strongest Byakhees. Screeching and Preying Byakhee are just more dangerous than Black Star’s Riftseeker.

Threat level: Low to Mid in Phantom of Truth, Low in Black Stars.

Dealing with it: An agility(6) test is not something that you usually expect to pass, so taking that test will mostly be aimed at failing as little as possible, to reduce the chance of having an enemy appear. After that it’s just flipping cards from the encounter deck, seeing what happens and possibly deal with the enemy.