Blue Dragon

Grab a lighter or something curved like that and rub it over the "A" button fast
Not only does this work FIRST time
...but its EASIER on your thumbs!

I wasted 90 minutes on this and the lighter trick worked first time =]

After about 20-30 minutes into the game (after your initial meeting with Nene), there will be a cut-scene where you'll be flung into an area to the top of the ship with a save point directly in front of you.

SAVE!!!

Advance to the glowing light pedestal where a cut-scene will begin. Near the ending of the cut-scene, 6-7 guard robots will appear. For me they just stood there while I ran off, so I suggest you to the same, preferably in the direction opposite the robot guards.

After running out of the room, you'll run down a hallway with an open door at the end. You'll be introduced to yet another cut-scene where Shu will run to a valve crank in order to shut the door. Here is where the first dexterity challenge comes in.

"Press the A button as fast as you can" is the goal. The challenge is split into three parts, each part split up by Shu groaning at the amount of strength required to turn the wheel. Tap A as fast as you can to fill up the bar at the top screen, and, when full, the door will close more. As I said, you must do this three times in a row.

If a single robot makes it to the door before the end of the third dexterity trial, you'll be pulled into battle and you will lose your chance to get this achievement. Simply reload from the save point you made prior to the first cut-scene and try again. If you succeed in closing the door without any robot battles, you'll receive this achievement and continue on with the game.

An alternative to the above solution, you could simply use your thumb and index finger to press the button quickly.

This method has worked for me on all games that require press a button rapidly, not just on Blue Dragon. Therefore this can be applied to all achievements similar to this one. It does, however, take some practice to master, but overall it is effective and easy.

Method:
Position your index finger and thumb finger as if you were trying to pinch something; or pickup a hair off of a table. The key is to assure your fingernails are covered by each other as best as possible to avoid them getting caught on the edges of the button. (It's best to use your dominate hand as the pinching hand).

With your other hand, brace the controller tightly and maybe even up against your stomach or chest. This is important to maintain consistency between your presses.

Execution:
Now, simply place your pinched fingers on the button desired (for this achievement, "A" button). Rapidly strafe your pinched fingers to the left and to the right of the button, approximently enough to almost touch the right joystick's protrusion (the part that begins to rise up from the flatness of the controller that leads to the right thumb stick) and as far right as almost hitting the edge of the "B" button. With practice, this motion can be easy and do the trick very effectively. The trick is to vibrate your center of gravity (based on your entire arm) at your wrist, letting your elbow sway freely. The energy thus goes into the fingers propelling a fast back-and-forth motion, and the energy also moves to your elbow, and transfers back into your wrist and then into your fingers. Try it out, and you will see what I mean!

Note: The back and forth swipes should be very fast and very brief. A good benchmark would be to aim for 6-8 presses per second.

Good luck!