There are 6 'sub-achievements' to unlock rampage, meaning that you have 6 different goals to accomplish to unlock one Achievement. You do not have to complete these goals in any specific time frame, as long as they are all on the same save file.
The 6 goals are as follows:
1. Blow up 25 gang-controlled vehicles in 60 seconds.
- Use rockets or grenades. Get a hit squad to come after you by killing enough gang members or a boss, get on a highway, and fire away. You can do this with parked and empty gang vehicles, but you can usually only find these cars in a garage, in which case you probably won't be able to get 25 of them in enough time.
2. Kill 15 gang members with your bare hands or thrown objects in 60 seconds
- You can easily get this in a Los Muertos boss location. Just jump right into battle and keep mashing . If you keep dying, wait until after you finish the game and max out your stats, then go back in Time Trial mode and do this.
3. Shoot and kill 15 gang members in 60 seconds
- Simply go into a boss location with a Harpoon Gun, which is available with the paid DLC, and fire away. You can do this with any weapon, but the Harpoon Gun is a one-shot kill for most enemies.
4. Use explosives to kill 25 gang members in 60 seconds
- This is the easiest one to get. Go into any boss location with a rocket launcher and some grenades, and blast away.
5. Use a vehicle to run over 10 gang members in 60 seconds
- Use the technique described in "Agency Wheelman".
6. Pop 20 tires on gang-controlled vehicles in 60 seconds
- This is probably the hardest one to get. Remember that 'gang-controlled' means that it must be a gang car, it does not have to be occupied. Go to a gang's garage, for example, underneath Cowell's building in Shai-Gen. Go in with a weapon with a large clip, pull , then press Down on to lock onto the tires. Rinse and repeat until you have 20 done. Try to get the 6-wheeled cars, as they go by in almost the same amount of time, and you'll only have to aim 7 times instead of 10.
You can view your progress on these at any time by going to the Pause Menu, going over to 'Agency Info', selecting 'Achievements', and scrolling down.