Here is a very simple example based on what you have said so far: Go down the script to about line 778 where the examples are and change it to something like this.
when 1
q[:name] = "The First Quest"
q[:icon_index] = 0
q[:level] = 0
q[:description] = "Slimes are overrunning the farm. I must eliminate them"
q[

bjectives][0] = "Kill 15 slimes. That is enough to stop them returning"
q[

bjectives][1] = "Report back to Peter"
q[

rime_objectives] = [0, 1]
q[:client] = "Peter"
q[:location] = "Muswell Farm"
q[:rewards] = [
[:item, 1]
]
Presumably you have set up a variable to count the slimes being killed.
So, it would go something like this. When your hero speaks to Peter and gets the quest, you do a script call in that event to :
reveal_objective(1, 0)
When the 15 slimes are dead, your next script call is :
complete_objective(1,0)
reveal_objective(1, 1)
When s/he speaks to Peter you have
complete_objective(1, 1)
distribute_quest_rewards(1)
And that's it.