Most enemies move around the screen, reducing Link's hearts if they manage to touch him, or in some cases hit him with a projectile. Many of them have other forms of attacks which affect Link in different ways, ranging from attempting to eat his shield, to cursing him temporaily.
The range of methods used to defeat ZC enemies is quite varied: some enemies are only vulnerable to certain items, some enemies must be attacked in a specific way to circumvent their defenses, and some enemies can't be defeated at all.
Some enemies are categorized as Bosses, although this is largely an unofficial categorization, since practically any type of enemy can be made into a "boss." However, the enemies which we usually refer to as "bosses" tend to be larger and capable of taking and dealing out more damage.