For multiplayer this would require
a) Use of a killed eventhandler on each unit on the map
b) The killed eventhandler would need to broadcasting the killer's identitiy to all clients
c) a receiving script on the client would check if the killer was himself and then increment a count to a variable
(Use of CoC_Ns would help here, although it is doable without)
For single player, this would be easier, no need for networking
When a unit dies that has a killed event handler attached too it, the eventhandler passes 2 variables to for example a script
this addEventHandler ["killed", {_this exec "unitkilled.sqs"}]
unitkilled.sqs
_u = _this select 0 (the unit that got killed)
_killer = _this select 1 (the killer unit)
then to broadcast it
tx_Killer = _killer
Publicvariable "tx_killer"
the receiving script would look something like the following
#start
@ !isnull tx_killer
? (tx_killer == player): goto "I_AM_KILLER"
tx_Killer = objnull
goto "START"
#I_AM_KILLER
tx_myscore = tx_myscore + 1
tx_Killer = objnull
goto "START"