I guess it depends on your definition of "going on a quest" is. There is no tactical element in the expansion. Meaning there's no minis on a dungeon tile like gloomhaven or descent, if that's what you mean.
Basically, there is one of 6 monsters to fight at the end after character generation is complete. And by fight, mechanically you will roll combat dice trying to do more damage than the other players. Each monster has a special ability that affects players rolls. The amount of combat dice rolled is dependent on meeting additional character creation goals. The goals are different every game and start out secret. The players get opportunities to peek at the additional goals throughout the character creation portion after defeating a minion. Going on a "Hunt" to fight a minion is an alternate option to buying a market card or discarding a market card. When you defeat minions you also gain a new resource called XP, which can be spent in a variety of ways.
Hope that helps.
Well yeah I wasnt expecting minis or anything like that and your description sounds exactly like what I was hoping to hear sooo yup I want that