Most of the violence isn't human on human, but instead involves massive destruction and millions of implied deaths.
Asteroid chunks hit a satellite and the man working on it. The man is then briefly seen cut in half (his lower half is shown briefly with some blood).
Although played for humour, Harry chases A.J. around the oil rig, firing a shotgun at him (and blowing out windows, etc.)
An asteroid falls to Shanghai,China drowning a lot of people.
A major meteor takes down Paris with a ground waved smash heading toward the screen. This is the most disasterous and intense scene in this movie.