There are plenty of giants who battle our heroes in almost every odd-numbered chapter, but there are also three other Big Bads worth mentioning.
On the Argo II side of things, there's Porphyrion the giant king, who has set up shop at the Acropolis, and, like the final boss of a video game, is just waiting for Percy and Annabeth to arrive. His goal? To use their blood to awaken Gaea, the Earth Mother who plans on killing all the gods and taking over the world, as titans tend to do.
On the mortal side, we have Octavian, a Roman who's organizing a war against the Greeks of Camp Half-Blood, coincidentally (or not) on the exact same day that Gaea is supposed to arise. This guy might even be worse than Porphyrion, actually. As a giant, Porphyrion was born evil. Octavian, on the other hand, chooses to start a war, in the hopes of gaining more power for himself.
Spoiler alert: all the bad guys are defeated in the end.
What have we learned from the bad guys? Always check your robes when operating explosive machinery.