Once you finish the "S.A.M mission" and return to the construction site you will automatically begin the "Ransom" mission. The ransom mission then directly leads to the "Exchange" mission. Once you have started "Ransom" get a fast car and drive it to the way point on the map. Park it just outside the gate facing uphill. This will save you some time once the mission begins. I also recommend having full health and full body armor before you step into the blue circle. All you weapons will be stripped at the beginning of the mission.
Once the cutscene ends you will be standing next to the guy Claude just punched and a pistol will be on the ground. Multiple enemies will begin shooting at you with automatics and will kill you rather quickly even with full armor and health. Quickly grab the pistol and run to the side of the house nearest you. If you are quick no enemies will follow but just in case turn around and shoot any enemies following you with the pistol.
From here there are two ways of going about the rest of the mission. You can either play as intended or use cheat codes. Both methods are really the same but if you don't use codes you need to stop and pickup weapons which is both time consuming and makes it more difficult because you can only use whats available to you. I am going to assume cheat codes are being used because most people do, if you aren't the strategy is basically the same except you need to pickup weapons. I won't bother listing every code here but you can find what you need here: http://www.ign.com/cheats/games/grand-theft-auto-iii-ps2-155...
Once you are on the side of the house use the codes to restore your health and armor but do it quickly because the mission timer has started. Move around to the opposite side of the house and quickly get into the Cartel Cruiser parked just in front. Drive towards the gate but stay slightly to the right so you can line up and run over the two gate guards. Once the gate opens drive outside.
A short cutscene will play showing a helicopter that you need to follow. Quickly switch to the fast car you parked outside the gate (alternatively you can just stay in the Cartel cruiser) and follow the helicopter across the bridge and then immediately right. Go over the dam and down until you see two Cartel Cruisers blocking the road. You can either get out and rocket launcher them or just drive thru the center of them. At the bottom there will be another roadblock use the same strategy.
Once through the second roadblock you will see a few enemies. I recommend sniping the two guards on the two towers slightly to the right. The rest of the enemies you can dispose of at will with either red barrels, assault rifle, sniper rifle, or rockets your choice but try to be quick as time is ticking away.
Once the first set of enemies in sight is down I recommend walking up the wooden ramp on the left and sniping as many enemies as you can in the second set. The reason for this is because a cutscene triggers once you walk forward and then you have to deal with them and its much easier if you thin out the herd first. Once you are finished walk forward and a short cutscene will show Catalina getting in the helicopter.
Three important things happen here. First, Catalina gets in the chopper and circles around to fire at you with rockets. This will take about 30 seconds but if she does and you are still on the ground it will instantly kill you. Second, an enemy gets in one of the trucks and tries to run you over. Third, any remaining enemies on the ground start shooting at you.
First things first pull out a rocket launcher and destroy the truck coming at you. Then quickly shoot any enemies still on your level and book it to the helipad stairs straight in front of you. You need to kill the truck and enemies and make it to the stairs before the helicopter can line up and fire rockets. There are 2 guards guarding Maria on the helipad so watch your explosive use. Shoot them and then get on the helipad. There is a rocket launcher there in case you need it. Use rockets to shoot down the helicopter. Once the heli is down walk back towards Maria and the final cutscene and credits will play. The trophy will unlock once the credits are over and you are transported back into the game.