I've just played the game today. It's sure fun, in my case.
Spoiler about boss battle(highlight): Strangly, the boss of this chap was a monster cake. Just stab him with those pointy things on the top on the place.

(PPF stands for Puyo Puyo Fever in this case.)
I have finally found a tactic that defeats all of my opponents: overload them with nuisance puyos as quick as possible before the enemy attacks or is close to Fever Mode.
( http://en.wikipedia.org/wiki/Puyo_Puyo_Fever for those who have no idea what I'm talking about.)
Though against Carbuncle, I'll surely fail with this tactic unless I was able to use Yu.

It turned out that I'm against Popoi as the final chalenger. T-T I was really expecting Carbuncle!! Oh well. I should be able to unlock the last secret character, somehow.
(In mid-battle.) Change tactic. Make the hugest chain against Popoi & Carbuncle & went thye start to send Nuisance, release the chain immediatly & repeat as quick as possible. In Fever Mode, just pop all of the link by doing a step-chain/fluent rensa.
Or
Huge chain in normal style & go into Fever Mode right after Popoi/Carbuncle then wait the him to finish his first chain after that you do yours.

Note that repeated all-clear step & power chains are the best.