Assassination Missions are unlocked shortly after making your way to Alderney in the main story. You'll receive a call telling you about the missions at some point after completing the mission "Truck Hussle" for Phil Bell. They can be accessed from a Payphone not far from the hospital in the center of the island.
The missions themselves are generally straight forward. As you might expect from assassination missions, you need to murder various people. Each mission is different though, so you'll need to listen to your instructions each time.
You'll be given some body armour and a weapon for every mission which you'll be able to collect in the yard behind the fence next to the payphone. You should always grab these items as they generally prove to be very useful for the mission itself.
The rewards you receive for successfully completing the missions are dependent on how well you've done on previous missions. The first three missions will add $3000 to your bank account per mission, however if you manage to complete two additional missions without dying, the money you receive will be topped up to $7000 per mission. Upon completion of the last mission you'll receive a $3000 completion bonus on top of that too.
Luckily the game is flexible about how this all works. If you die during a mission, you have four real-time minutes to get back to the payphone and accept another mission. If you manage to do this, you will not lose the bonus you have acquired. If you do break the chain for more than four minutes, then you'll receive only the $3000 flat fee payment for mission completion.
Please note that the missions are in random order, and most likely your mission order will be different to the ones below.
Hook, Line And Sinker
The Fixer wants you to take out a guy on a boat to the North East of Westdyke. Grab a vehicle and make your way to the red marker on your GPS.
Once you arrive, you'll be told to find a way to the target who is out at sea. Luckily there's a boat waiting for you in the water, so climb aboard and make your way out to meet the target on his boat.
As you approach, he'll try to escape, so chase after him and drive-by both the driver and the gunner inside the boat. Once they're both dead, Niko will call the Fixer and explain that the file is closed.
Fixer wants you to take out three targets in Acter Industrial Park, so grab a vehicle and head to the red dots on your GPS.
Once you arrive, you'll find out that there are far more than three targets. Make your way into the compound and climb up the stairs towards the top of the multi-storey platform nearest to the road.
Once you reach the top, you should be in range to auto-aim at the enemies with an M4 or AK-47. Take out the ones you can get to, then a few of them will attempt to escape and head down the stairs. Lock onto any of the ones you can see, and shoot at them as you move downstairs. Once they get to the ground floor it shouldn't be too difficult to take out the remaining enemies who will charge straight towards the tower you're in.
Mr. Fixer wants you to kill three men who have been lured to an old building in Alderney City. As usual, grab yourself a vehicle and make your way to the red GPS location.
Once you arrive, you'll see a load of guys standing around on various floors of the building you need to climb up. They don't seem to take too kindly to you being there, so you'll need to dispose of all of the enemies in this area, as well as the three you've been assigned to kill.
Head up the various floors of the building and kill all enemies on that floor before proceeding to the next one. There's a health pack on the wall half way up if you need it.
Once you reach the top, kill all of the remaining enemies and once the last target is down, Niko will call the Fixer and inform him of his success.
Fixer explains that the target he needs to be eliminated is above the Booth Tunnel. Head into the yard and grab the body armour and weapon he left for you. This time it's an RPG that you'll be able to obtain.
Make your way towards the booth tunnel, and as you approach the helipad on top of it, you'll be told to take out the target before he escapes. Whip out your rocket launcher and aim it at the helicopter, but don't fire until the target is just about to get onto it. Once it's made contact and blown up, Niko will call the Fixer.
The Fixer explains that your next target is on a boat in the canal to the South West of Alderney. Head into his yard and grab the Sniper Rifle he's left you, then get a car and make your way towards the boat's position.
Pull up on the waterside and whip out your sniper rifle. The target is a girl on a boat in the water. Wait carefully for the boat bobbing so that the target is right in your sights, then take the shot. Once she's down, Niko will call Mr. Fixer.
Fixer tells you that this target is in a car moving around Alderney, and he needs to be taken out. Grab the sub machine gun from the yard, then get a vehicle and make your way to the red dot on the GPS.
Once you catch up to the vehicle, you'll be told to separate the convoy. All you really need to do is spray SMG bullets through the rear left window of the limo. Hit the guy in the head and kill him, then high tail it out of there.
Bailing Out For Good
The target is just being release from the police station in Alderney and the Fixer wants you to wipe him out.
Make your way to the police station and you'll see the target run out of the building. Gun him down, then get out of the way of any cops who will shoot at you.
The target is in Alderney city, and you've been taksed with eliminating him. Grab a vehiucle and apprach the GPS location. Once you get close, the target will escape in a Patriot and pull into an alleyway. Follow him into here carefully, it's loaded with enemies. Take cover behind your car and move into the area taking out the enemies one by one.
Once they're all down, Niko will call the Fixer.
Fixer tells you that the target you need to take down is in Acter Industrial Park, so grab a vehicle and follow the GPS to the location.
Once you arrive, you'll find a drug deal going down with some guys on bikes. Try to toss a grenade into the middle of them, but if that fails, and I predict it will, switch to an M4 or AK-47 and take them down. You may want to fire a few shots into each of the people on bikes to prevent them escaping, then when they fall down, take them out.