Quests and Contracts are available from the Quests and Contracts Board in the Inn when you are at level 7. Quests can be completed by apply the correct number of keys. Keys are earned through contracts. Every day there are two key contracts available.
Quests are the in the top left. Try to take one quest that doesn't need many keys. The two key contracts that you can do each days are directly beside the quests.
The achievement will unlock when the right number of key contracts are completed for your quest and you complete the quest by going to the board.