From Halopedia, the Halo wiki
The Killing Spree medal is awarded for killing 5 opponents in a row without dying in multiplayer and Spartan Ops. In campaign and Firefight it is awarded for killing 10 opponents in a row without dying. In Halo: Spartan Assault and Halo: Spartan Strike the medal is awarded for killing three enemies in a row without being hit.
The Killing Spree medal was represented by a steel 4-sided star with a cyan target in the middle, with the Halo 5: Guardians version having a cyan colored star. In Halo: Spartan Assault and Halo: Spartan Strike it is represented by a stylized shield. When a player gets this medal the announcer will shout "Killing Spree!" to the player that received it. In Halo: Combat Evolved, because there are no medals, if a player kills five opponents in a row without dying, they will still hear the announcer, but instead see "Killing Spree!" in the upper left of the screen.