Which... we are? Bakuda's working for Coil, remember? This isn't an "oh hey while we're here" sort of thing, Baku-chan supplied the weapon Coil used to try and kill us -- and did kill everybody else in the fucking building. We've got justification aplenty for taking her down first, fast and hard.
Tattletale? She's a squishy. If she isn't chained up in Coil's dungeon she'll be in the wind thirty seconds after she realizes Calamity Witch is in town, and if she really is pulling against Coil she won't tell him before she bails.
Wrong subordinate. Bakuda's not someone who needs to know very much to do her job. Lisa doesn't need to know too much either, but she has a thinker power which makes information control harder.
I'm not saying don't hit Bakuda, I'm saying hitting Lisa,
then Bakuda would have been better. You go in with more information while depriving Coil of one of his options. Also, meta-knowledge-wise, it's the better strategy against Coil's power.
Coil's power is indeed formidable, but it's actually very easy to beat. Don't think of it as fighting a person, think of it as fighting a computer algorithm, one that always goes for what improves its current situation. Algorithms like that have one ENORMOUS weakness: they're vulnerable to local maximums. In essence, put it in a situation where the only way to actually win is to take the worse option.
As for why I'm bringing this up in the first place despite it not changing anything, it's a teachable moment. I'm a QM myself, and this is a perfect example of what I call the id-ego-superego of quest protagonists.
The id is the options the QM gives you. They're simple, not terribly creative, and easy for the QM to control.
The superego is the players. This usually follows the id, but can also come up with outside-the-box solutions to problems.
And finally, the ego is where the QM interprets things.
Moral of the story?
Do not trust the id. I've deliberately left the "right" answer out of the options before in my quest, because I wanted the players to
think. Now, it's possible Silently is less interested in creative players than I am, but I doubt it. A good QM has the most fun when the players are doing something they don't expect.