From what I remember, whenever I was stuck, I would visit the park and dig up random stuff. You can get free gifts that boost your heroine's heart level there. I'm also pretty sure boosting any heroine's heart level gives you a stat value increase, and this sticks with you regardless of what heroine you're partnered with. Gifting is the fastest way to increase the probability of the heroine's skill. I recommend using a weapon that gives you a lot of cards to choose from, because many times you will have to settle for draws to build up your combo. If you haven't already, there's a secret dungeon you can gain access for one-time only; this dungeon is tedious, but stacks permanent stat boosts for each fight you win, and this dungeon can only be accessed by donating enough currency to Sebastian.