HT Games
Positioning
Play one of the first stages, which shouldn't have any bombs or obstacles to prevent you from getting a flower. This is especially useful for the Silver Star and Black Pearl achievements.
Line Formation
Search for a cluster of four like-colored hexes, preferably near the bottom center of the board. These should be arranged in a C formation. The positioning is important because it frees up the rest of the board for making cluster matches.
C Formation
Rotate a cluster with two more pieces of like color into the C shape. Since there are a limited number of possible moves on each map, this might take some experimentation with rotating in each direction or clearing nearby clusters. When the two final pieces rotate into place, the center piece will glow and change into a silver star.
Stars and Pearls
Stars can be rotated and stacked in order to produce Black Pearls, associated with another Achievement for "Hexic HD." Paradoxically, it is easier to use a silver star to create another star flower, since the hexes around the silver star all rotate at once.