A secondary character may have been crushed by a dinosaur off-screen in the Prehistory chapter. In the Near Future chapter it's likely people have been crushed by the living statue and mech fighting each other, but we don't see it.
Akira’s father dies in a shootout prior to the events of the Near Future chapter- another character’s father also dies in a boss battle partway through the same chapter, having been converted into a robot under the villains’ control
The entire Distant Future chapter can be considered claustrophobic, as it takes place in a spaceship with no possibilty to escape from a threat. In some sections the main character gets stuck in an even smaller space and has to escape.
It depends on your perspective - in the Near Future chapter's final sections you use a mech to fight plane-like machines, so they crash if you defeat them. They are treated like any "monster" you fight though.
Several instances of "shit," "bullshit," "asshole," and "son of a bitch" in the Wild West, Present Day, and Near Future chapters. There are also two censored f-bombs in the latter two, and one character in the Wild West chapter insists the player character can't handle milk "'less it's fresh from [his] mother's tits."