Not a dog, but the huge bear that seems to be a friend of vagabond Logan does die. The hunters who shot it do not finish the job, and it becomes Logan’s task to put the old grizzly out of its misery with his claws.
Mariko's father hits her multiple times. I put it here instead of in child abuse because she is an adult for the duration of the film and there are never flashbacks.
The thing on Logan's heart resembles a chestburster from alien with less organic features. Could be triggering to people with instectophobia or severe arachnophobia.
Logan operates on his own chest to remove a small robot creature preventing him from healing properly. the scene is fairly short but very graphic (not very anatomically accurate) and relatively plot important.
There are instances of seppuku in the very beginning, the alternative to which is dying in the Nagasaki bombings. It is not a choice between life and death, it is a choice between death and worse death. Logan also catches a distressed Mariko as she attempts to jump off a cliff.
There is a flashy explosion in the beginning and any time they're in the main Japanese family's home there's lightning, and the end fight scene has flashing