Battle mode is almost literally impossible at battle 3 and 4. Other wise an absolutely awesome game, I've drawn every character except for the characters on the last two levels as I cannot unlock them.
Ok i will try to make it easier.
Always try to upgrade as early as possible by matching 4 or more in a row. Upgraded characters do more damage. Also try to get combos for multi damage. Some characters have special abilities like destroying the characters left or right, moving left or right or up etc.