I created a mission where you need to blow up 10 different weapons Caches. All the Tasks are listed at the start of the mission, so you can complete any task you choose.

I want the players to be able to complete the tasks in any order, so how do I make this work with an End Mission Trigger to fire after all Tasks are complete?

You can make 10 different boolean variables and set them to true when a task is completed. Then end the mission only if all 10 of them are true.

For example :
init.sqf

obj1 = false; obj2 = false; ... obj10 = false;

And each time you get a task done :

obj1 = true;
publicVariable "obj1";//just in case

Then something to check:

if(obj1 && obj2 && ... && obj10) then {
    forceEnd;
};

Or if you want the end in a trigger, just set the condition as mentioned above end set the type to End1.

Much easier is to name all the triggers that have to be activated for the mission to end,
Then create a final trigger and enter put in its activation: trigger1 && trigger 2 && trigger3 etc.