UPDATE: 10/14/2016 - The bomb-defense video I linked was missing; replaced it with a video showing the same technique
The key to this achievement for me was creating a Master Grid. There's a great picture of it on hexic.info. IMO, don't bother with the 4x4 grid. It's vulnerable to accidental combos, whereas the Master Grid protects you from them. I failed quite a few attempts at this achievement because I'd lose starflowers while trying to repair a collapsed 4x4 grid.
Before even thinking of starting the grid, you'll need to develop a few skills:
1. Making Starflowers
To make a Starflower you must surround one tile with a ring of 6 tiles of any same color (except the color of the center tile). This takes some practice, but it gets easier. Look for places where you think you can make a starflower, then look nearby on the board for places you can make simple combos (3 tiles) that will rotate pieces near or into position for your Staflower.
2. Learn how rotating Starflowers triggers combos
Really what you want to do is learn how to avoid making combos. First, look at the ring of 6 pieces immediately surrounding your star. Next, look at the ring of tiles immediately outside of the ones you can rotate with your star (it's a bigger ring, with 12 tiles). Anywhere you see two of the same color touching on the same ring is a place where a combo could be triggered. For example, if you have two blue tiles touching on the outer ring, watch out if you have any blue tiles on the inner ring.
If you have two of the same color on the inner ring, pay close attention to any tiles of that color on the outer ring. If the tile has a corner pointed toward the center of your star then you'll make a combo if you rotate. If tile on the outer ring has a flat egde pacing toward your star then it's safe to rotate.
When you get two Starflowers touching you can use them to rotate each other and move around the board. This can help you to create more Starflowers, which is the key to starting your grid. Star-walking is decribed on hexic.info and is shown in the videos I've linked, so look on of those places to see how it works. Practice Star-walking while avoiding combos and you'll be able to make the Grid and get this achievement.
There are several tutorials on YouTube on how to set up the master grid. The one I found most helpful is the linked below (first link). Pay particular attention to the two key moves: the Parallel Turn and the C-Turn. These are absolutely key to moving stars into position with minimal risk. You're most at risk of an accidental combo / grid collapse when doing these moves, so look carefully before you move.
If you manage to get a grid built, you've got most of the hard work out of the way. Your biggest threats at this point will be rebuilding your grid after you make pearls and bombs. Repairing your grid is exactly the same as building it, so just keep at it. And for bombs, check out the second video for a way to instantly kill any bomb by setting up "Multipliers" in the top-left corner (the video explains this well). Just make all of your new Starflowers on the second-from-left Starflower. The video just shows making simple combos there, but if you make Starflowers then the bombs will still always drop in the right spot.
If you make it this far, you should have "no trouble" making enough Pearls for your Pooh-Bah. Just be careful rebuilding that grid! Good luck!