The Black Bombs are triggered with the colored bombs that your Fiends throw.
Blowing up a Black Bomb with a Green Bomb!
Notice that as you drag a colored bomb, white outlines (or targeting circles) indicate which blocks it will blow up. Make sure these targeting circles line-up with the Black Bomb to blow it up. You'll know that the Black Bomb and colored bomb are correctly aligned when all the blocks in the level are highlighted by targeting circles.
Black Bombs are very strong and will blow up everything breakable in the level.
e.g.: Charge your Green Fiend, Temper, with green leaves and he will throw a Green Bomb. Match this Green Bomb with other green leaves and release your finger when its targeting circles line-up with the Black-Bomb.