Need help with a proficiency system(experience system)

I am a newb, so take this with a grain of salt, but I think your problem is pretty solvable. You should be able to know the amount of damage caused, inside the weapon script that calculates damage to apply to your enemy.

If you spawn a AK47 bullet prefab and send that at an enemy you will likely have to make a decision about what is the damage amount associated with getting shot by an AK47. I would assume that that logic is in the script for your weapon or bullet.

Then you could OnCollisionEnter or OnTriggerEnter when the bullet hits the enemy and have the bullet damage variable of the projectile or gun decrement a health variable on your enemy.

Since you will probably be doing some passing of variables from one script to another and between scripts on different gameobjects you will probably need to familiarize yourself with GetComponent. This is a really useful functionality that will allow you to access and change variables in other scripts. Combining this with OnTriggerEnter you can do things like 'When this hits something, change variable X in script Y of that something"

The larger point is that unless there's some complicated calculation or damage modification happening inside the enemy health script (because of armor maybe, or taking different damage for diff body parts) then you should know your damage amount from the start and be able to take that same number and add it to your proficiency tracking script.

Good luck!