Have another variable isWithinObjectiveTime which is set to 1 as soon as the objective starts, and set it to 0 after the objective time has ellapsed. You can do something like this
And then add a condition to check if isWithinObjectiveTime is 1 in the event that checks for a kill.
I'm guessing you want to have multiple objectives at the same time. In that case, you should create an 'Objective' object, have objectiveTime and isWithinObjectiveTime as instance variables, and try using the timer behavior (which does the same thing as Every X seconds, but on an individual level for each object