You will encounter a variety of monsters throughout the dungeon, some more ferocious than others. All monsters have a different method of moving around. Some fly through the air, while others are bound to the ground. Some monsters move all the time, and some remain stationary. There are even those monsters who stand still until you touch them, and then they come to life. Most monsters are vulnerable to attack immediately. However, there are a few monsters who must be touched first in order to cause them harm. Attacking them before you allow them to attack you will do no good.
Touching a monster will hurt you (with the exception of Pochi). All monsters that are killed leave an item behind, usually a beneficial one unless it's a vial of poison. While you may be tempted to destroy every monster you see, bare in mind that monsters can sometimes be useful for reaching areas in a dungeon that are otherwise out of reach for particular characters. This can be most easily seen with Pochi, who can touch monsters freely without penalty. For every other member of the family, you may find that touching monsters may in fact allow you to find shortcuts to new areas if you risk sustaining a small amount of damage. It's a good idea to look for such opportunities.