Rampages can only be done by the one and only Trevor Philips aka everyone's favorite hipster... but anyway... there is 5 in total and are marked as an orange skull on the map. Below I have provided how to achieve gold on all 5 missions:
Rampage 1:
45 Kills
3 headshots
Destroy 2 vehicles
Rampage 2:
45 kills
6 headshots
Destroy 2 vehicles
Rampage 3:
50 kills
6 headshots
Destroy 2 vehicles
Rampage 4:
45 kills
6 headshots
Destroy 2 tanks
Rampage 5:
30 kills
10 headshots
Destroy 2 vehicles
Note from old solution on Xbox One below:
TwiK999 would like to add that "the first rampage doesn't show up as a skull. It shows as a strangers and freaks mission. Its one by the Alamo Sea."