How do I make this script work in a part with a click detector?

First of all the methods you wrote are case sensitive so it won't work the way you wrote them. The proper way of writing getPlayers is GetPlayers.breakJoints is supposed to be BreakJoints. Make sure you Check the Object Browser in Roblox Studio to check all the events,methods and properties for each object. Help-->Object Browser.

If theMouseClick event is fired then it will connect the function and run it.

function ClickTime(Plyr)
for i,v in pairs(Players:GetPlayers()) do
v.Character:BreakJoints()
end
end
script.Parent.ClickDetector.MouseClick:connect(ClickTime)

Make sure the ClickDetector object and the script are inside the Part.

local detect = script.Parent.ClickDetector -- Assuming the script is within a part, and the part has a ClickDetector in it

function kill()
        for i, v in pairs(game.Players:getPlayers()) do
        v.Character:breakJoints()
end

detect.MouseClick:connect(kill)