As you start, head to the sewer entrance to the south east with the Point of interest flashing, head down, and pick up the rat poison. From there, head to the building with the small door, on the North East side of the map. Head up to the fifth floor, and as you see a Blue Lotus guard, head into the room to the right of you. Ready your silencer, as he'll be coming in after you! Shoot the guard, and take his clothes, so you can make it into the park to poison the tea. Be careful that no one can see you, and poison the tea sitting on the ledge of the rotunda. Best to get out of there discreetly straight away heading for the exit point on the map... On the way, your status will change, and you can hightail it out of there!
[NOTE: The previous editor claimed that you can shoot Lee Hong and take his clothes. Come on! Does he even appear in this mission? And can you take Lee Hong's clothes? I don't think so...]
Alternate Method 1
Once the mission starts make a run for the 5 story building across the street from the park on the east side. Go up the stairs to the second floor -- you go to the door to the left and pick the lock. Inside you will see a table with a bomb and detonator. Take them immediatly and get out of the room before the tenant returns. If said tenant is already in the room when you arrive, you will have to sedate him. You then exit the building and head over to the southside of the park where the Red Negotiator's limo is locate. You cannot plant the bomb on the side of the limo! The bomb must be planted on the driver's side which is under close watch by the guard at the westgate of the park. Get as close to the gate and then make a run along the wall to the west. This should cause the guard to redirect his attention to the west and away from the limo. Run all the way around the park until you return to the southside again. Go into sneak mode and move up to the car--the gate guard should still have his attention directed toward the direction you ran earlier. Plant the bomb on the car. Once that is done, head back to the 5 story building and run all the way up to the fifth floor. Don't worry about the guard on the 4th floor--he is just guarding the entrance to the room with one of the few vantage points to the park. But you won't be playing sniper this round. Continue to the fifth floor, go into the room with the gardener suit, change into gardener suit, and leave all your guns behind including your sniper case. Run back downstairs and exit the building. Walk into the park--guards will search you at entrance. Walk over the where the Red Negotiator and Blue Emissary are talking and wait til the Blue Emissary steps away for a bit. Walk up in front the Red Negotiator, make sure nobody is watching, pull out your fiberwire to show to the Red Negotiator, and put the wire away a split second later. The Red Negotiator will look at you shocked for a split second and then take off for his limo without alerting the guards. Run from the park and exit on the eastside. Run to the east until you see the road leading toward the east exit. The Red Negotiator's limo will be leaving in that direction. As soon as the limo drives under the tunnel, take out the detonator and set off the explosive. This will destroy both the limo and the Red Negotiator. Now exit the same way the limo tried to go. Mission will end with Silent Assassin.
Alternate Method 2
Another method (which is easier) is to go to the building with stairs leading to the dirt roof and the tree, put down the suitcase on flat ground there, crouch so there is not as much sway and wait for the red negotiator once you see him (it may be a bit hard but you should be able too). Shoot him, put the sniper rifle back in the case, and walk to the exit (if it went how it went for me while your walking away you should get a message saying the blue emissary survived).
NOTE: I did this on the HD collections version, this may not work like this on other version. PS: Also works in the PS2 version.
Silent Assasin in two minutes
Here is my walkthrough for "silent assasin" run in two minutes.
First go to the bottom of the map where the "ladder" drawn. Stand close to the wall the way Blue Lotus Guard near the ladder wont notice you. Wait till the guard will turn and use syringe on him. Take his clothes and get up on the ladder. Now you have a view on the target. Get your sniper rifle, make one precise shot on Red Dragon negotiator (make sure you won't hit the Blue Lotus negotiator) and head to the exit.