for the impossible badge (assuming you have all upgrades) it helps if you only use the bomb when the boss only has ~25% health. if used at the start, you spend the rest of the battle fighting the 'harder' part of the boss (as a boss loses health, their attacks get faster etc.) whereas if used at the end, you never have to fight the 'harder' part of the boss.
some tips (finally got the hard badge):always watch the fastest moving ball. more than likely, it will be the cause of your failure. never stop moving, it keeps your hand warm and makes sure your ready for when you have to really move. migrate to sections of the arena where the balls aren't. that way you can see what's coming and the balls waste their energy on each other. lastly, do what suits you. i found i was able to do with my own music playing so i could just relax and subconsciously do it but for others, this might do the opposite.
 "Epic Boss Fighter"){kind=icon}
 "Dojo of Death"){kind=icon}
 "Bubble Sky"){kind=icon}
 "Band Of Heroes"){kind=icon}
 "Symbiosis"){kind=icon}
 "Snail Bob 2"){kind=icon}
 "Particles"){kind=icon}
 "Papa's Hot Doggeria"){kind=icon}
 "The Great Siege"){kind=icon}
 "Ghost Guidance"){kind=icon}
 "Dibbles 3: Desert Despair"){kind=icon}
 "Papa's Pancakeria"){kind=icon}
 "Diamond Hollow"){kind=icon}
 "Proke"){kind=icon}
 "The Ocean Around Me - Week Two"){kind=icon}
 "The King's League"){kind=icon}
Smart strategy ;)