Death on the Mississippi
This is a fairly easy mission, as pretty much all of the targets can be pushed over the rails to their death in the alligator-infested water. The only challenge is Skip Muldoon, as he rarely leaves his quarters and so cannot be pushed over a rail unless your timing and/or patience are impeccable.
Killing the Gator Gang
They are the easiest targets in the mission. Despite there being six of them, they tend to foolishly stand near potentially dangerous areas. If you see any Southerner biker-looking trucker hat-wearing blokes standing near rails, chances are that they are a Gator Gang member, 5 them wear same outfits.
You start at the front of the ship. Run up the stairs and inside. Go through the double doors in between the stairs. Along this corridor are key card-locked rooms. You'll see one of those biker-looking trucker hat-wearing guys in the corridor having a good time with his lady. As you approach them, they stop and take their "conversation" into the gang member's room. Wait a while and you'll see him come back out alone. Follow him outside and he'll stop and lean against a rail. Now's your chance. Run up to him and push him over the edge. The body falls over the railing and off of the boat. Sometimes a lady is taking a break at the balcony. After a while, she will leave. A direct method of dealing with this member is to wait nearby for the lady to leave his room. Once she exits the room, sneak in past her while the door is still open and you will notice the gang member has his back to you, an opportune moment to garrote him. It is important to note that the lady leaves the room to smoke outside to the left side of the ship, she returns on occasion to rendezvous with the Gator-gang member with full access to his room. If you have killed/sedated him, she will most likely spot the body on her return.
Once this gang member is done, run back to where you started and go further along the deck. You'll see a walkway to your left and a group of crates directly ahead. If there is nobody around, then you'll have to wait a bit. Once there is a sailor there, get behind him and take him out. Quickly hide his body behind the crates and take his clothes. Now you can go back to where the walkway is and into the engine room.
Occasionally, another gang member will choose to come take a look around the engine room. He'll walk around, and eventually come to a stop and lean on a rail near some machinery. I think you can guess what to do here, but in case you can't, push him into the machinery once nobody is looking. Incidentally, this gang member can be the first one you'll encounter if you to go up the stairs. He should be walking from the right corridor and will descend down the stairs you go through. A rather difficult, but straightforward way of dealing with this member is to push him down the last set of stairs. If you're very lucky, he'll die on impact. If not, which should be most of the time, he'll only be knocked out. Either way, you must dispose of the body and this can easily be done by dragging him to the edge of the ship to throw him overboard. This method is unorthodox and difficult to execute, due to a ship guest standing overhead the stairs who may overhear the gang member fall resulting in her calling for help. Another problem is the ship guards who frequently make their rounds on both sides of the deck, who may spot you dragging the body. Timing and positioning is important in this method, and the positioning of potential witnesses can be dispersed if the player 'stalls' the gang member by constantly bumping into him as he makes his way down the stairs. This method can be done if the player prefers to deal with this particular member immediately, rather than having to be patient in the engine room. A rather easier way to deal with him is to run up the stairs at first and stalling the Gator in the corridor until a guard had passed both of you. Now fiber wire the Gator and throw his body over the rail (if you are too close to the stairs, drag the body a bit into the corridor before dumping it).
Otherwise, get your silenced pistol ready, the Gator Gang #2 should be in the 3rd deck, looks like he is having fun with a lady, it is no fun to us however, you can either kill him while she is out of the room (she will come back, so you will need to knock her out before she does) or use her as human shield and kill him quickly and quietly before he raise the attention, the latter method is quite risky but very clean. If shooting is not your favorite and you want to melee him, wait a little longer and let him come out of room #309, follow him outside and you can finish him, but beware of guards nearby.
Gator Gang member #3 can be found patrolling the staircase leading up to the captain's deck. To get past the guards, you can climb the white trellis found around the outside of the boat. Like the two before him, he can be dealt with by pushing him over the rails. However, he may land on a lower deck and be found by another guard so be careful, don't leave his body on the 4th deck, or it will be found. You can dump it when you are out of sight, then it will no longer be a problem.3 down, 3 to go. #4 can be found guarding the door to get inside the captain's quarters. He can be sorted with the fiber wire. Be careful though, as there are other guards that frequent the area.#5 gives some variety. You can poison/sedate the hamburgers in the kitchen to sort this guy out. If you sedate him though, you will have to throw him over a rail to make sure he dies. This guy will also risk falling to a lower deck though so watch out. Alternatively, he will go to bathroom for a piss every few minutes, take this oppotunity and fiber wire him, you can use this place to dump bodies, as long as you do all this without rasing attention.
#6 is the same as #5. he will eat the hamburgers and die (or get knocked out). However he must be dealt with as he goes to the side with a 1st Class Purser.
Note that it is difficult to use the poisoned hamburgers effectively since the plate comes with three burgers and 47 only has two doses and you have no way of knowing which of the Gators will eat poisoned burgers. You can combine both type, and finish the knocked out one. Also, if you plan to kill Muldoon with poison, the dose will also be lost.
The big guy now. Skip Muldoon. He likes to remain in his quarters with one of the 1st class pursers who takes a shower for the whole time. Anyway, if you've taken care of the Gator Gang, this guy is pretty easy to deal with, as the gang members won't be in the area to impede you. If you haven't yet, there is a risk the Gator in green steps in and sees you. He will go out his quarters for a short period, use this timing if you like to create accidents.
You can either go right into the quarters when Muldoon isn't looking (the map will show you if he's looking away) and fiber wire him. Also, you can wait around the side of the quarters for Muldoon to come out (yes, he actually leaves his quarters!) and fiber wire him or push him over the edge. If you push him over the edge, he will likely land on a lower deck.If you're feeling super sneaky, you can grab a 1st Class Purser uniform, poison the cake in the kitchenand deliver it to Muldoon. Make sure you have no weapons on you before entering, as the one guard outside (who, in fact, is your other target) will search you. Luckily, it's possible to hide one item in the cake (the gun is recommended). However, you will need to get his showering friend out of the way for this, as the friend will likely come out from the shower if you deliver the cake to Muldoon (this is one of the only times the friend will stop showering).
If you take care all the Gator Gang members before dealing with him, you can wait for him to use the bathroom and use the shower guy as a human shield to gun him down.
Once Muldoon is dealt with, and the rest of the Gator Gang is either strangled or eaten by alligators, you must open the safe in the side room of the captain's quarters and raid it. Once you have the documents and you are sure all your objectives are fulfilled, go back down to the third deck. The exit is on the south end of the ship, at the boats, approach the boat then you will see the exit point. Remember to dodge the engineers and the guards - they can often ruin your rating in an otherwise perfect gameplay.