Pippin slayed a troll at the Battle before the Black Gate Of Mordor.
Pippin shows honour & pride in the last few paragraphs of the chapter titled, "The Black Gate Opens" in Return Of The King. He also shows great courage. As Pippin draws his sword, he thinks to himself;
'This was made for just such an hour,' he thought. 'If only I could smite that foul Messenger with it, then almost I should draw level with old Merry. Well, I'll smite some of this beastly brood before the end. I wish I could see cool sunlight and green grass again!'
Though showing great courage, he also shows defeat. He see's it as a foregone conclusion that he's going to die, along with everyone else in Middle Earth, but he still chooses to fight.
"At Pippin's side, Beregond was stunned and overborne, and he fell; and the great troll-chief that smote him down bent over him, reaching out a clutching claw; for these fell creatures would bite the throats of those that they threw down."
Beregond is Pippin's friend from Gondor, another Guard of the Citadel, whom helped when Faramir was in danger of being killed by his father. The troll was about to kill him, and Pippin had to act.
"Then Pippin stabbed upwards, and the written blade ofthe Westernesse pierced through the hide and went deep into the vitals of the troll, and his black blood came gushing out."
Pippin had managed to kill the troll using the sword he got in the Barrow-downs, toward the start of the trilogy (in the chapter called "Fog On The Barrow-downs" in The Fellowship Of The Ring). However, the troll was large and heavy, and it fell once Pippin has destroyed it.
"He toppled forward and came crashing down like a falling rock, burying those beneath him. Blackness and stench and crushing pain came upon Pippin, and his mind fell away into a great darkness.
The words, 'The Eagles are coming!' remind Pippin of the tale Bilbo told to him - the story we know as 'The Hobbit'. He remembers how the Eagles came in Bilbo's story, and rescued Bilbo, Gandalf and the Dwarves when they were trapped up some trees, surrounded by Goblins and Wargs, and rescued them. He decides that that was Bilbo's story, not his, and that the Eagles would not rescue him as they did Bilbo.
Luckily, Gimli found him on the battle field - spotting only his foot, though for a Hobbit, that was enough to identify him - and the Dwarf pulled the troll carcase off him, along with many other bodies. Gimli thought he was dead to begin with, but realising it was not true, he bore Pippin away to be healed. So, those of you who dont like Gimli - you better like him now!