INTRO
It’s not a good idea to use .Touched for damaging stuff, it relys on physics and most of the time it’ll be inaccurate. If this big enemy we’re talking about swings a sword, it might be best to install a Raycast Hitbox Module, which is here: Raycast Hitbox 4.01: For all your melee needs!
OTHER SOLUTIONS
You could use Raytracing to detect players getting hit by Big Enemy. The link I provided has a code example, so you should be good.
GENERAL CODE REVIEW
if game.Players:GetPlayerFromCharacter(hit.Parent) then
local player = game.Players:GetPlayerFromCharacter(hit.Parent)
local CanBeDamaged = hit.Parent.RemoteHit:InvokeClient(player)
This part has quite a bit of flaws. Firstly, the if game.Players:GetPlayerFromCharacter(hit.Parent) should be saved into a variable, to prevent further yielding and visible “hops.” Also, when you call :InvokeClient on a RemoteFunction The scripts yields waiting for that response, so essentially, a exploiter could override the Invoke callback on the client and break your entire script.
The part where when we can apply damage to the player also has a flaw, you should really save the Damage module in a local reference, rather than requiring it every time, which would be extremely expensive (I think.) when using physics-based events.
IN ALL,
Don’t use .Touched for hit detection, it’ll save you tons of headaches and testing.