The Titan’s Curse by Rick Riordan

It's not everyday you find yourself in combat with a half-lion, half-human. But when you're the son of a Greek god, it happens. And now my friend Annabeth is missing, a goddess is in chains and only five half-blood heroes can join the quest to defeat the doomsday monster. Oh, and guess what? The Oracle has predicted that not all of us will survive...