For example, if you hit a man in the face, cause bruising, lets say that costs $1,000 across the board. $1,000 for any hematoma, $5000 or any broken bone. $25,000 for a GSW, $100,000 for a life-threatening injury, etc.
To take it further, if you discharge a weapon at another human being, the fine is something like $1,000 per bullet, etc.
Additionally, existing laws still apply.
Following the above guidelines, you don't need to prove mens rea. It is just the cost of doing business.
It would be a violence tax at the individual level.