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User01322342, I described this in the FAQ section of my signature. Quests have the ability to customize stages:
ProgressCommentsFileRef – if the quest consists of several stages (for example, kill 3 groups of monsters), you can add files with additional descriptions for each stage here. In the game, the general description of the quest from DescriptionFileRef will be displayed first, followed by the description of the current stage from ProgressCommentsFileRef. If the quest has stages, it will start at stage zero.
-- quest progress
-- progress – the stage number corresponding to ProgressCommentsFileRef
SetObjectiveProgress(‘SCRIPTED_QUEST_NAME’, progress);
You can check for monster kills using a trigger at the end of the battle. The quest must be custom.