This huge, horned dude attacks Percy, Grover, and Sally Jackson as they try to get Percy safely to Camp Half-Blood for the first time. The Minotaur nearly kills Percy's mom, making Percy furious. Percy rips the Minotaur horn off and kills him with it. This is remarkable, considering that Percy has no formal training when it comes to fighting monsters – yet.
FYI, Pasiphae was the wife of King Minos. One day the gods sent King Minos a beautiful bull, expecting him to sacrifice it to them. King Minos didn't do this. As a result, his wife, Pasiphae, had a baby with the bull: the Minotaur.
Check out the Minotaur's mug shot here.