Lots of mass destruction and collateral damage throughout, but none of it is bloody nor is any explicit human injury shown.
Level of violence:7/10.
PG-13 violence type: blood and gore.
Concussive explosions, demolished buildings, riddling bullet sprays, roaring lasers and heat beams, and all manner of scenery-destroying action are the order of the superday. The alien attack causes rubble to fall on screaming, running crowds, and it's implied that Metropolis is nearly leveled from the impact of incredibly destructive alien beams, human military bombings and strafes, and the collateral damage of superpowered beings smashing through entire city blocks of concrete and glass and steel as they pound, pound, pound each other in extravagantly ultraviolent ways. Cars and trucks are picked up and tossed like crumpled wads of paper.
Children scream and gasp for air as their bus slips beneath the water of a lake. Lois is struck by a menacing robotic arm, and we see a small circle of blood stain her shirt. Clark catches her and cauterizes her stomach wound with his heat vision. A man is caught in the swirling winds of a tornado. Pilots tumble out of their crushed planes, and people fall out of demolished buildings.
On Krypton, we see Jor-El and General Zod fight, the two aliens battering each other viciously. Zod ends up with a slashed wound on his face, and he ultimately kills Jor-El with a large-blade stab to the abdomen (just offscreen).
From a distance, a pilot in an aircraft has his head squeezed until it pops and bursts into a gory mess by the side character Nam-Ek, a moderate amount of blood splatter can be seen but is mostly covered by the shaky camera work and messy focus. This scene is very brief and easy to miss because of the distance.