Chapter 4 " The beginnings of an idea- a tiny hopeful, fire- started forming in my mind." (page 78) This means that Percy is thinking about going to the underworld to find his mom.
Character vs Technology
Chapter 4 " As the monster barreled past ,I drove the broken horn straight into his side, right up under his furry ribcage." (page 55) This means that Percy Jackson killed the minotaur.
Character vs Nature
Chapter 8 "On the other side of the creek ,the underbrush exploded. Five Ares warriors came yelling and screaming out of the dark." (page 120) This means that Percy has to fight five Ares warriors by himself.
Character vs Character
Chapter 1 "I wasn't aiming for the school bus ,but of course I got expelled anyway." (page 2) This means that Percy blew up the school bus.
Chapter 2 " Come on. What? I said. Its thousand degrees in there." (page 26) This means the bus was really hot.
Chapter 6 "Water shot out of the toilet ,making an arc straight over my head, and the next thing i knew, i was sprawled on the bathroom tiles with Clarisse screaming." ( page 91) This means that Percy has water powers and attacked Clarisse with water.