Characters
Sell one-star and two-star characters as soon as you have your team filled with three-star or better characters. Power your team members up often. Use found books to level your characters up. Enter the "Enhance" and use potions to increase health and attack stats, elixirs to get enchantments, and access the evolve and merge abilities.
Combat
Build your skill meter and save it for Bosses. Manage your links carefully throughout quests and save enough of them for Bosses. If removing pieces you have already highlighted will cause matches to fall into place, there is no need to use links to connect them. If you are careful about which pieces you remove, you can do a lot of damage with a small amount of moves. The colors you are matching are important. When the colors of the pieces match up with one of the elements, it causes all characters of that element to attack. If you do not have anyone with a matching element, removing those tiles will not be that helpful. When using a mixed team, going for the strong attacks is generally a good strategy; however if the enemy only has a small amount of health remaining, it may be better to use up some of the tiles they are strong against to remove them from the board. The more tiles you have on the board that can target the Boss's weak point, the better. Try to win Boss fights as soon as possible. Expend any buff skills you have available, then use all your links to throw as much as possible at the Boss. Close your loop to eliminate any henchmen. After that attack, use skills that restore links to allow another forceful attack. If you do not have anyone with a healing skill, save heart tiles to recover after the Boss's attack.
Elements
Use an element that the enemy is weak against to do double damage. Elements also are a factor in determining the damage you receive when enemies attack, as well as certain active skills. Most of the storybooks rely on one element more than the others. Keep two or more each element type leveled up and ready. It is possible to keep a full party of each element.
Characters...