Multiplier Mining: Do 5-piece combo's as often as possible - don't make Starflowers because you have to get rid of them later. Best way to make 5 piece combo's in case you aren't sure is to put either a Starflower or Black Pearl in the 6 o'clock position with the other 5 pieces all the same color. Research has shown that 3-4% of pieces dropped are multipliers (on level 7) so the more pieces you "exchange" per bomb round the better.
Black Pearls: Sorry, but I would abandon that game and try again if you have 3 "Y" pearls only. It's a glaring weakness with Hexic that you can't choose which kind, but it is what it is. Best possible scenario is to have 1 of each kind of pearl.
Bomb Defense: Traditional Defense (keeping 2 like colors together near the top) is effective but time consuming. The best bomb defense is the "Multiplier Bomb defense". Keep 3 mulitipliers together in the top left or top right corner of your grid. If a bomb drops that you don't have the pieces available to kill the traditional way, move your bomb so that it is next to the 3 multipliers. Cluster the multipliers and they create an explosion that will take out the bomb (and all pieces directly touching the 3 multi's).
And don't forget, if you ever get a bomb that looks unkillable, post a picture of it here - someone is sure to take a look and help you out.
Best of luck with your game.
R.I.P. Phoenix
Veteran: COD2 / COD 4 / COD WAW / COD MW2