Grand Theft Auto 3

Helicopters are non-driveable vehicles in the game that come in two variants. The first is the police helicopter which you will see once you obtain a three star wanted level, and the other is the normal helicopter which is seen in some of the later missions in the game. Helicopters can easily be shot down and destroyed with the use of a rocket launcher. If you wish you can use cheats to obtain the rocket launcher as well as to increase your wanted level. Alternatively it can be purchased from Phil’s armoury in Staunton Island later in the game for $25,000.

The easiest way to obtain this trophy is to first obtain a three star wanted level by killing people, cops and blowing up cars. You will want to be somewhere away from the main roads so you don’t have to worry about police cars running you over and you can focus on shooting down the police chopper. I found the sawmill location in Portland near the bridge to be the best as you have to climb a fence to get inside. As such, no cops will be able to get to you or be able to shoot you so you are free to focus on the choppers. There will likely only be one police helicopter at a time, and once it has been shot down another one will appear. Simple repeat this five times for the trophy. You don't need to destroy all five in one go, but they do need to be on the one save file.

The below video shows the above mentioned location and method of how to obtain this trophy fairly easily.