The new monster Servum is shown attacking people at multiple times throughout the movie - they violently kill people, but generally no bloodshed. However, it is very intense and could be frightening to younger viewers. Servum picks up people with their jaws and jostles them around violently, sometimes they swallow humans full.
In the flashback in the beginning of the film monsters are shown attacking cities. It is not scary at all, but there is major destruction.
In the final fight, Godzilla kills some minor characters via atomic breath, EMP, or indirectly (one man falls off his speeder when trying to retreat from Godzilla and falls to his death) some of them cut away before the result but other deaths show it head on.
Godzilla destroys an escaping ship, presumably killing many people.
A person commits suicide by gunshot to the head, it happens offscreen but we see blood splatter the wall.
The scenes on the spaceship are very grim and depressing, as it shows multiple people suffering from starvation, disease, and depression. A ship contained with elderly people explodes because of a planet's intense atmosphere.
Godzilla is shown killing multiple people, including the main characters parents.
A man commits suicide onscreen, and it shows it in full capacity - it doesn't cut away when he pulls the trigger, and we see his body slump over and blood splatter on the wall.