In chapter six, on page 77, it says "None of what happened was Grover's fault. I also felt really, really guilty. If I hadn't given Grover the slip at the bus station, he might not have gotten in trouble." Percy was telling himself that it was his fault that Grover got in trouble.
Character vs. Nature
In chapter six, on pages 90 and 91, it says "Clarisse bent me over on my knees and started pushing my head toward the toilet bowl...Then something happened. I felt a tug in the pit of my stomach. I heard the plumbing rumble, the pipes shudder...Water shot out of the toilet... hitting Clarisse straight in the face so hard it pushed her down..." Percy and Clarisse were having a fight.
Character vs. Society
In chapter four, on page 48, it says " My mother threw herself against the driver's-side door. It was jammed shut in the mud. I tried mine . Stuck too. I looked up desperately at the hole in the roof. It might've been an exit, but the edges were sizzling and smoking." Percy, Grover, and Percy's mom were stuck in the car and couldn't find a way out.
Character vs. Supernatural
In chapter one, on page 8, it says, "Overhead, a huge storm was brewing, with clouds blacker than I'd ever seen over the city." There was a big thunderstorm forming.
In chapter five, on pages 67 and 70, it says " 'Wait,' I told Chiron. 'You're telling me there's such a thing as God.'.. ' Ah, gods, plural, as in, great beings that control the forces of nature and human endeavors: the immortal gods of Olympus'...'But they're stories,' I said... 'They're what people believed in before there was science.'..'Science!' Mr. D scoffed...'You're a god.' 'Yes, child.' 'A god. You.' He turned to look me straight on, and I saw a kind of purplish fire in his eyes, a hint that this tiny plump little man was only showing me the tiniest bit of his true nature." Percy didn't believe in the gods while everyone else at the camp did.
In chapter four, on pages 54 and 55, it says "The bull-man charged too fast, his arms out to grab me whichever way I tried to charge...I couldn't jump sideways, so I leaped straight up,... landing on his [the creature's] neck... I got both hands around one horn and I pulled backward with all my might. The monster tensed, gave a surprised grunt, then----snap!" Percy was having a battle with the Minotaur.