Treasure hunt is accessible from the "Games" menu. From the main map screen, press "Y" to open the menu, then select "Games" by pressing "A."
To play Treasure Hunt, you'll need Treasure Maps, which are awarded for some quests, and available in the shop for 30 Glory. You also get a map for a cascade of 5 chain reactions in any game (to borrow a Bejeweled term).
Treasure hunt is another match-3 game, but you only start with 8 moves. Matching 3 symbols uses 1 turn.
The good news? Matching 4 symbols does not consume any turns and matching 5 or more adds a turn!
Every 15 turns you take nets you a random traitstone as a bonus.
Matching 3 like symbols gives you one of the next symbol in the progression. It is worth noting that the new symbol will always take the place of the piece you just moved, while the others disappear.
The progression goes like this: Copper coin - Silver coin - Gold coin - Brown bag - Brown chest - Green chest - Red chest - Vault. You need 2 of these vaults in the same game to unlock the achievement.
Strategies: I like to work top-down, making 4s and 5s. If I have to make a 3, I make it near the bottom to shake up the board above.
-Always make a 5 if you can, even if it seems to mess up your short-term plan. Turns are your most important resource.
-Confirmed that you cannot earn more than one extra turn per cascade, so it's best to make a 5-match near the top of the board, rather than lower, if there's an option.
- Sometimes, the pieces just don't fall your way. Don't get frustrated. You're earning gold, souls, glory, and keys just for trying!
-Treasure Hunt does not award any XP.
The achievement unlocks at the end of the game, after all other rewards are given.
Kooky Cow 32
You might want to add that if you have the troop 'Tyri', you have a 20% chance to get a treasure map every time you use her move. I've gotten 2-3 maps in a single Quest game before. Not only gives you more chances at getting this achievement, but also gets you a lot of rewards!
I believe you get Tyri as a reward for completing all Quests in Zhul'Kari, though I'm not 100% sure, someone would have to double check that. But if that is how you get her, it's one of the earlier Kingdoms you can unlock, so I would advise doing so right away as the rewards you can get as a result are pretty insane!
Edited 6/29/16: Starting moves reduced 15 to 8. Traitstones now awarded every 15 moves.
Edited 12/16/16. Starting moves seem to vary. Possibly based on guild levels.
Edited 12/17/16. Additional starting turns can be earned by donating to the green guardian under the guild tab. Turns seem to be awarded at a rate of one per 10 guardian levels.
Edited 12/30/18. Changed method for accessing Treasure Hunt.