While playing drums, go into "Training" from the main menu, then into "Drum Trainer", and then finally into "Drum Lessons". Drum Lessons are a collection of drum rhythms to get you accustomed to some of the nuances of playing drums (using your limbs independently and such).
(Note that this is separate from the "Beatles Beats". That's another achievement entirely.)
There are 45 drum lessons and to get this achievement you need to score 100% on all of them. And it has to be a real 100%. If you hit every note but accidentally hit a pad twice during the rhythm, you'll score 100% but it won't count the lesson as completed.
Most of the rhythms are pretty simple but the later ones can be tricky. It's important to note that you can complete the drum lessons at ANY BPM. If you want to start out fast but then get stuck on a beat somewhere, just dial down the BPM meter with the D-Pad. You MUST complete each Drum Lesson at the minimum tempo of 60 BPM. (Correction added - thanks Nighthawk205) You'll know when you've completed a lesson when at least one of the drum icons on the left side of the screen turns gold.
EDIT: I should also mention that in the Achievements menu in the game, there's a checklist of the beats that's listed on the right hand side of the screen when you go to this achievement's entry. It updates automatically by checking off each rhythm you've completed so if you're unsure of which lessons you have yet to complete, you can consult this as well.