To easily get the achievement of "Hexic Addict" and "Complete 100 games of Hexic", go to Time mode and start a game on the Normal difficulty setting. Get at least one cluster for the clock to start. Then, wait for the time (50 seconds) to run out. This counts as a full game. You can do this as many times as needed to get the "Hexic Addict" and "Complete 100 games of Hexic" achievements.
To get the achievement of "Flower Child", you must form a flower cluster. The easiest way to do this is the wait until you see a partially formed one (four or five pieces of the flower already together). Then, drop in the last piece and you will have created a flower. Flowers are worth a lot of points. Make a flower whenever you get the chance to do so. Note: Do not destroy anything beneath a partially formed flower, or the flower will break apart.
To get the achievement of "Star Gazer", you must form a star cluster. The easiest way to do this is look for a partially formed star cluster (two pieces) and just drop the last star piece in whenever one gets close enough to the cluster. Also, the pieces in a star cluster do not need to be the same color; they just need to be star pieces. Forming a star cluster also gives you a lot of points and usually a large combo. Note: Do not destroy anything beneath a partially formed star cluster, or the star cluster will break apart.