If I recall correctly, the Portrait of Ruin doppleganger is actually effected by everything you have equipped - not just your weapon. So if you walk into the room "naked," and then equip your most powerful stuff, you'll have absolutely no trouble beating it.
The doppleganger in CV3 transforms a split second after you if you switch to your partner during the fight, and it's vulnerable for a split second after it takes on its new form. So if you continually switch to your partner, wait for the doppleganger to morph, attack, then switch to your partner and repeat, you can (cheaply) beat it without taking a hit. That's actually the only way I've ever beaten it.
In the fight against Dmitri in Dawn of Sorrow, you can attack him with a soul that flies overhead in an arc pattern. He'll absorb it and attack you back with the same soul, and you can safely duck underneath it. I don't know if this can be considered an exploit, though. I think that's the way the designers intended for the player to beat him.
The most common CV exploit is probably the fight with Death in CV1. Hang onto the Holy Water for the Death fight, and get a triple shot before you get to him. When he first appears in the top-right corner of the screen, you can toss Holy Water on the platform in that corner and he'll be stuck until it burns out. Keep tossing Holy Water there as fast as you can, and Death will be dead in seconds.