How do I clear a dungeon?

Each dungeon contains 10 or more "dungeon rooms".

To clear a dungeon, you must clear all dungeon rooms without dying or quitting the game. If you die or quit in the middle of a dungeon, you will need to start over next time.

To clear each dungeon room, you must kill all enemies on the map. 

These are indicated on the top-right corner of the screen.