1. Start up Brain Games (second page of the menu).
2. Hit RB until you're at Game 19 and press A.
3. Using the left analog stick to highlight buttons, press A with the following buttons highlighted:
Happy Birthday
9-9-8-9-6-7+7+7
9-9-8-9-5-6+6
9-9-2-4-6-7-8
3-3-4-6-5-6+6.
In the original manual, where I've placed the pluses are where you're supposed to hold a beat for more than one count. So if you count "1" for each single note, if you see 7+7+7, hold down the A button while you count to 3. I don't know if you actually need to long-hold, but I did just to be safe. [reports say the long hold may not be required, or at least may be very lenient - thanks, Mr Rodster!]
After you finish the last note and let go the achievement should pop.
In general, the controls are hyper-sensitive here so it can be frustrating. Just keep at it and you'll get it.