Half-minute Hacker Achievement
Completed the 15 Puzzle within 30 seconds.
This achievement is the sole reason I rated this game a 6/10 in difficulty rather than a 3/10. 30 seconds truly is an absurd time constraint and the mini-game is a complete departure from every other bit of gameplay in Final Fantasy. But I want to stress that it can be done with only a little practice. You can beat it legitimately or use a solver; I'm not convinced that one way is actually any easier than the other. But know that the achievement is not as intimidating as it seems at first.
You can access the 15 Puzzle after you have crossed the bridge out of the starting area and made your way East to Pravoka. Once there, you must obtain the Pirate Ship by defeating the Pirates on the West side of the town, and speak to their captain, Bikke. He will give you the ship in the harbor just South of Pravoka, and thereby, access to every harbor in the world. Once aboard the ship, hold one finger on the screen of your phone, and use another finger to tap the screen 23 times (no timing is required, though the game may not register if you tap too fast). This will prompt you to play the 15 Puzzle, with prizes rewarded in-game for fast puzzle completions.
I have written up an explanation of 15 Puzzle, as well as a tutorial for successfully beating it legitimately, which can be found by clicking HERE. Let me stress that it only took about 2 hours of focused practice for me to get quick enough to obtain the achievement legitimately; it has less to do with intelligence or reflexes, and everything to do with muscle memory.
There is another strategy for unlocking the achievement, which is to utilize a web-based solver. I have not tested this method, but it makes sense and is apparently the more popular way to earn the achievement. Unfortunately, you should note that a PC (or Mac) is required to use the solver. I have been totally unable to find one that is compatible with any sort of mobile device (and believe me, I tried). Anyway, for this method, you would start the puzzle, then either hold the WP back button to access the phone tabs, or press the Windows button at the bottom center of the phone and then hold the back button. This pauses the game, but still allows you to view the puzzle, and enter the configuration into the solver. Note that puzzles which require many steps (the maximum optimal number of steps is 82) are likely just not possible, and will have to be reset to find a more favorable configuration. Once you have found a fast-completable puzzle (50 steps or fewer), then memorize the first few steps, bring up the tab with the paused game, complete the steps, pause, read the next few steps, and continue until the puzzle is solved. Many have posted that this way isn't particularly easy, so don't be discouraged if you don't get it in your first few tries.
The most popular solver for this method can be found by clicking HERE.