Two kinds of quests are currently available: Forest Trail and Big Dig.
Forest Trail quest is an event in which you complete levels on a forest path to uncover a treasure. If you fail a level, you do not have to start over; you can retry it for the duration of the event.
Big Dig quest is an event where you play levels to get a shovel for the Hatchling. Once a level is completed, you can decide where the Hatchling will begin digging in the sand. The goal is to find all the keys to open the reward chest. Even if Hatchling doesn’t find the key in the hole you chose to dig, you won’t be left empty-handed, as you will get other rewards, such as boosters and coins from the holes that do not have a key inside them.