Instructions
Play through the "Halo 3: ODST" video game normally until you reach the level that takes place on the roof of the NMPD headquarters. You will eventually pick up Buck as an ally in the game, and he will follow you through missions until you reach this point.
Position yourself on the roof of the building so that you are facing both Buck and the ledge of the building. You should be facing Buck, and Buck's back should be to the ledge of the building.
Shoot Buck one time with your gravity hammer. Because Buck is an ally, your shooting him will not cause him any damage. However, the force of the blast will still knock him backward. This moves him closer to the ledge of the building.
Continue to shoot Buck with your gravity hammer until he falls off the ledge of the building. The fall kills Buck instantly.