How do I add this to the boss battle script?

Alright, I'll answer for you.

So, to start off, you only want it to activate when a player walks over a part.

I won't watch the ENTIRE tutorial, so go ahead and correct me for any mistakes.

First of all, disable BossHandler in the boss. Then, disable the BossHealth GUI.

Then, make a part.

Insert this script:

local boss = workspace.BossNameHere -- Replace BossNameHere with the name of your boss (also make sure it's in the workspace)
local ts = game:GetService("TweenService")
local fadeTI = TweenInfo.new(1, Enum.EasingStyle.Quint, Enum.EasingDirection.InOut)

for _, i in pairs(boss:GetDescendants()) do
	if i:IsA("BasePart") then
		i.Transparency = 1
	end
end

script.Parent.Touched:Connect(function(hit)
	if hit.Parent then
		if hit.Parent:FindFirstChild("Humanoid") then
			local plr = game.Players:FindFirstChild(hit.Parent.Name)
			
			if plr then
				for _, i in pairs(boss:GetDescendants()) do
					if i:IsA("BasePart") and i.Name ~= "HumanoidRootPart" then
						local t = ts:Create(i, fadeTI, {Transparency = 0})
						t:Play()
						
						t.Completed:Connect(function()
							boss.Head.BossHealth.Enabled = true
							boss.Head.BossHealth.BossHandler.Disabled = false
						end)
					end
				end
			end
		end
	end
end)

That's basically it. If you want an explanation, ask and I will gladly give.