All Quest objectives appear at the top right corner of the User Interface, along with a short description of what must be completed to achieve your goal as well as the Quest's Star Rating. The Star Rating tells how difficult a quest is, with one-star requiring you to defeat mini-bosses and three-stars requiring you to defeat a dungeon's master boss. Completing a quest will grant experience and cause a chest to drop near the location that the boss first appears. If the Star Bar is not completed already, you will be granted some gain for that as well.
Once you've completed a Lair or Dungeon, a large red "X" will show on the map and in the world hovering over the site, indicating to other players that it's been cleared. (This X can be destroyed by Lasermancy, however, so be on the lookout for trolling players.) Checking the map and overworld for these X's is a good way to make sure you're not wasting time exploring something that's already been looted.
The amount of experience and loot dropped varies based on the world level you're in.
One star quests are the sole objective of Lairs, and one of three objectives for Dungeons. When included in Dungeons they're always optional, and players can feel free to run past if they don't feel like engaging. In Lairs, however, they must be defeated to clear.
One Star Objectives
One star objectives are usually simple and straightforward. One of the most common is "Activate the Cursed Skulls," where players will need to navigate the Lair and find the Cursed Skulls. To clear it, you'll need to activate the skulls with "E", or attack it, and fight through two waves of enemies. After all of them are defeated the objective will complete and the gold chest and loot will drop.
Similarly to the "Cursed Skulls", some lairs have swarms of enemies players must eliminate. The Cursed Skulls appear just like in normal lairs, but once activated, many weak enemies emerge. Players must kill either 10 or 30 of them. Enemies cannot reach more that 5 at the same time, however there is no wave system: after one of them dies, another one takes his place instantly.
Another star objective is to defeat a mini-boss. This mini-boss can be found on the way to the main boss in a Dungeon, or in separate lairs. Mini-bosses will always be creatures appropriate for that biome, and will sometimes manifest minions to join the fight. The chest dropped by mini-bosses contains similar drops to the totems, but the chest is blue and gold. Recipe Lairs have their own unique chest that spawns instead, a gold and white chest with a recipe on the lid, which contains a recipe based on the biome of the dungeon.
"Unity Dungeons" are small open spaces with three golden statues. These dungeons are different from the rest for two reasons; first, three players are required to complete, and second, there are no enemies in these dungeons. As soon as three players reach the dungeon, the quest is completed, and a chest appears. These dungeons are usually avoided by solo players, but are a fast choice for groups doing challenge or simply completing dungeons.
Lastly, there is the "Dark Heart" dungeon, found only in Sky Realm and some dungeons in the Cursed Skylands. These lairs have no enemies, but also no chest and very little experience. Once players activate the "Dark Heart", many boxes appear. Players have approximately 30 seconds to break as many boxes as possible; for each box broken, they receive one radiant shard. Boxes are like chests, but smaller and take only one hit to break. Boxes appear in hard places, and players have to parkour their way to reach them.
Peaceful Dungeons are lairs that appear in the Peaceful Hills biome. They have no chest, enemies, and give no experience. They also are not part of any quest. They provide players with Sunlight Bulbs and Pumpkins.
Three Star Objectives
Three star tasks appear only in Dungeons. Players must wander through the Dungeon until they find the boss, which will be the strongest and highest leveled monster in the zone. This boss is usually in the largest and last room, and almost always has lower leveled minions accompanying it. The boss can also summon other minions after the first have been killed (See: Boss Modifications). After being defeated, the Dungeon will be cleared and a red and gold chest will drop. This chest often contains better loot than that found in gold chests, and gives the player more experience. Shadow Arena chests spawn as a blue and black chest with VFX.
(Note: Chests that drop from Uber may vary depending on the chest and level.)