You want to talk about "not for the squeamish"? The first shot of The Killing of a Sacred Deer is a horrifyingly long closeup of open heart surgery. Whether it's the most graphic image you'll see in the film is not something I'll reveal here; the point is that the shot not only sets up the story, it also sets you on edge, so that you are never sure just how far Yorgos Lanthimos is going to go this time. (Anyone who's seen his previous films Dogtooth and The Lobster should already know not to trust him.)
I will say this much: It's indicated that this surgery, performed by Dr. Steven Murphy (Colin Farrell), was not successful. It's also indicated that Martin (Barry Keoghan), the strange teenager who Steven has recently been spending time with, is the son of the patient. The nature of Steven and Martin's relationship remains purposefully unclear for some time. What's really going on isn't spelled out until halfway through the film.
It would be criminal to say more, though if you're up on your Greek mythology – and Lanthimos and his regular cowriter Efthymis Filippou are, as you might guess, Greek – the title will clue you in to the plot. (The myth itself is offhandedly name-checked in the film, in case you hadn't figured it out by then.) What the film is actually about is murkier. There's something about playing God, and a skewering of the modern family that connects Sacred Deer to Dogtooth. I'm not sure what it all adds up to, though. Mostly, the film is an indulgence in Lanthimos's signature style, with purposefully stilted delivery of mundane dialogue, creeping Kubrickian shots and sounds (absent a proper score, Johnnie Burn provides a chilling atonal soundscape), and pitch-black absurdist comedy. I'm on board with his approach; many will not be.
If you're new to the work of Yorgos Lanthimos, I'm not sure I'd start with this film. Frankly, I wouldn't know which of his films to start with. Oh hell, go ahead and start with this film. But be warned: it does get brutal.