The second quest I have devised for the Dark Age of Sigmar is the Lich's Eye. Each quest is a personal mini-campaign that you can play through to build a fun pulp story for your warband. In this quest, your leader has come into possession of a Lich's Eye and seeks to use it to harness the power of immortality.
With the skirmish Quests, I am aiming to make each one totally different. So where the Lake of Blood grants your general a special Command Trait, the Lich's Eye is an Artefact carried by the general that gives them a bonus spell.
The Lich's Eye quest also takes a totally different approach toward the quest's completion. The general must slay one model from each Grand Alliance to acquire the necessary spell components. They do still have a Final Challenge though, in which they must slay the enemy hero in combat.
In addition to the Lich's Eye quest for the Dark Age of Sigmar, I have put the quest mechanic to (hopefully) good use during Malign Portents with the Quest for Hammerstadt (I probably should have named it "Fate of Hammerstadt" or something, but so it goes).
In the Quest for Hammerstadt, I have presented my players with three different motivations for their warband, each of which deals with the exploration of the ruined city of Hammerstadt (the setting for my Dark Age of Sigmar supplement). Each of the three signs has three different objectives, and players start with the first, and check off objectives as they win battles. So in each battle each player has two ways to earn Laurels of Victory, their current objective, and their opponent's current objective. After Malign Portents is over, I'll tally up the signs of the players who completed the campaign and that will determine the future of the Ruins of Hammerstadt!