How do I increase a player's score when they kill something?

Hello, I am having trouble figuring out a way to increase a value in a script in the player's ScreenGui. What I need to do is detect who the player is who dealt the lethal blow to the enemy (or even better, whoever dealt the most damage) and then increase their money value by an amount, but I really know how to detect if the enemy died or who killed it. Thanks.

EDIT: I'm going to post the code that I have for the player's balance of money.

local Players = game:GetService("Players")
local ThePlayer = nil

function onPlayerAdded(player)
	ThePlayer = player
    local Coins = Instance.new("IntValue")
    Coins.Name = "Coins"
    Coins.Value = 166
	Coins.Parent = script
    if ThePlayer.PlayerGui.ScreenGui ~= nil then
      ThePlayer.PlayerGui.ScreenGui.CoinAmount.Text = Coins.Value
    end
end


--When a player joins, call the onPlayerAdded function
Players.PlayerAdded:connect(onPlayerAdded) 

--Call onPlayerAdded for each player already in the game
for _,player in pairs(Players:GetPlayers()) do
     onPlayerAdded(player)
end

while true do
	script.Coins.Value = script.Coins.Value + 1
	ThePlayer.PlayerGui.ScreenGui.CoinAmount.Text = script.Coins.Value
	game.ServerStorage.CoinGet:Play()
	wait(1)
end

For testing purposes, the amount of coins is increased by one every second.