The easiest way to do this is to make a cluster, as it only takes 3 Black Pearls, where as a line is 5 and flower is 6. Since Black Pearls are more difficult to make, that is why I say go for the cluster. Some of the methods below are untested, but are worth a try nonetheless. This achievement will take some time and patience, and unless you were able to create a Grand Pearl Poohbah in the original Hexic, don’t expect this to be a cakewalk.
1. (Courtesy of El Capitaine) Create a link of 8 stars (make a line, preferably vertical, of 4 stars, leave a colored hex in between, and then have 3 more stars on top. Then, rotate a star into the middle.) What this will do is create 4 rubies, because the game will see 4 simultaneous lines of 5. (1-5, 2-6, 3-7, 4-8). Then make a link of 7 stars (somewhere else, to avoid accidental clusters) to get 3 more rubies. Line them up either so that there is either 3 on each side or 4 and 2, with a colored hex in the middle. Then, rotate your 7th ruby into that spot. The game will see 3 lines, and give you 3 black pearls. Use emeralds, other stars, or just keep rotating until you make these 3 into a cluster.
2. Create as many Starflowers as you can in the beginning levels to avoid having new colored tiles and bombs get in the way of creating them. From there, begin chaining together your Stars to make Rubies. Once you have made enough Rubies to create 3 black Pearls, do so. I suggest making one at a time, that way you don't accidently make clusters. Also, do not use all your stars at once. Always make sure that you have at least 2 Stars to be able to continue making more, as you progress it will get more and more difficult to make Stars.