He kept up Dumbeldore's Army, finding how to transport members into the school despite the danger of snatchers and Death Eaters in the castle, who were open about wishing to torture him for all the times he acted out and refused to do the dark arts asked of students in their classes. When he met up with Harry, Ron and Hermione he is visibly beat up from all the actions he has committed against the death eaters at Hogwarts and narrowly escaped worse. He was one of the group that tried to steal away the sword of Gryffindor from Snape-possibly to try to get to Harry.
He faced down the Dark Lord, as mentioned before with the "I'll join you when hell freezes over!" when he is offered not just his life, but power within the ranks of the Death Eaters. Voldemort even notes his bravery. Neville has shown bravery before. He's not the smartest or best wizard, but even Dumbeldore noted his bravery from the first (remember, he stood up to his friends, concerned with the honor of Gryffindor house) and the bravery in the OOTP(couldn't cast due to broken nose, stabs with wand instead), and being one of the first ready to join the DA and fight.
Neville showed bravery again and again and the fact he did not even hesitate when the sword showed up, grabbed it and sliced of Nagini's head in one fluid movement.