Yuki Yamazaki is one of two people that have to be eliminated in "Situs Inversus". You can do it with style, using one of the available Opportunities, but this is not mandatory. I've brought all the best methods together below.
Note - The order of elimination is arbitrary, however if Erich Soders dies first, Yuki will stop visiting the garden in order to meet with the director of the spa. It may complicate matters if you've decided to eliminate her using a sniper rifle.
- Throwing Yuki into the abyss during her yoga sessions (Hot Springs Opportunity)
- Eliminate Yuki during her smoke break (No Smoking Opportunity)
- Serving Yuki Yamazaki a poisoned fugu fish (Thrill Seeker Opportunity)
- Other attempts to poison Yuki
- Locking Yuki up in a hot sauna
- Killing Yuki by approaching her in the director's outfit
- Eliminating Yuki through an explosion
- Sniper kill
- Cutting off the cable car with the escaping target
Throwing Yuki into the abyss during her yoga sessions (Hot Springs Opportunity)
This method doesn't require you to act quickly, as Yuki won't begin her yoga session until you pose as an instructor and meet her. First, you need to prepare the scene - visit the Yoga grounds (M8,21). You can read the schedule of Yoga sessions, but this is not mandatory. Start with getting rid of patients enjoying the hot springs. Find a wrench, which can be found in the garage on level 0 (M8,4). The garage is accessible for every employee at the compound.
Once you've got the wrench, visit one of the employee rooms that neighbor the spa (M8,23). Find a cold water valve and turn it off using the found wrench.
Now for the instructor's outfit. The instructor constantly roams between two areas - the level 0 garage (M8,10) and small rooms located by the main part of the spa (M8,22). The latter area is much more usable, as in case of the garage you would have to eliminate the mechanic working on the snowmobile, and there is always a possibility that someone will see your actions.
Once you've got the disguise, find Yuki and meet with her to begin her lesson. Return to the yoga grounds in the sauna (M8,21). Her bodyguards will stay behind, while your previous action has cleared all the other guests.
Approach the marker, and press the button to begin the session. During the lesson, press the buttons appearing on the screen to make Yuki attempt new figures. Finally, the target will stand on the footbridge. Press the last button - 47 will throw her of the bridge, and Yuki will die.
Eliminate Yuki during her smoke break (No Smoking Opportunity)
This method involves eliminating Yuki during her smoke break. Her habit is revealed through a conversation between her bodyguards standing by the cable car (M8,3), but you can just as well proceed without eavesdropping on the guards.
Begin with finding the cigarettes, which are one of the forbidden items in the clinic. The easiest way to attain them is to visit Amos Dexter's apartment (M8,2) . There are two ways to access it - either find a doctor's gown, or leave your apartment through the window, and use the ledge to enter his apartment. The cigarettes are on one of the tables. Other methods are not so glamorous - you can break into one of the shelves in the hospital unit (M8,38) (if you have a crowbar) or attack one of the workers walking behind the hospital unit (M8,9) and get the item from them (you'll need to take care of his body, which may prove to be problematic).
Smokes cannot be given to Yuki directly - you'll need to put them in one of two available locations. She has an empty pack lying in her apartment (M8,6). Only her bodyguards can access her room - for example, you can try to subdue one of the guards standing by the cable car. Once you've accessed the apartment (make sure that Yuki is not there - she will see through the disguise!) replace the pack on the table in the main room.
Yuki should notice the cigarettes once she returns to the room, and will go to the balcony to smoke (M8,7). If you want to use this Opportunity, eliminate two guards in the area by throwing them off the balcony. Once Yuki stands by the handrail to smoke, push her off the balcony. The Opportunity will be completed, but you may be detected by her personal bodyguard. Other approaches to this assassination include accessing the balcony of the neighboring apartment (M8,3) and making a shot when Yuki leans on the handrail (I recommend a weapon with a silencer).
The second place to leave the cigarettes is less obvious, and requires extra attention, but guarantees eliminating Yuki without any unwanted attention. In this case, you'll need to get the director's outfit. You can do so by using a poison (simple rat poison will do the trick) on the meal found in the restaurant (M8,17) (use a cook outfit if you want to stay anonymous) and eliminate the director once he rushes to the toilet (M8,16).
Make sure that you've gotten rid of all forbidden items, and visit Yuki's booth in the restaurant (M8,18). Let the guard frisk you, and leave the cigarettes on the table.
Your job is not done yet - you need to reach the garden and find the area with a red fuel barrel (M8,20). Punch a hole in it using a screwdriver (you can find it on footpath behind the hospital unit (M8,5) or in a small room next to the morgue (M8,8)) so a part of the fuel spills out. That's it - wait until Yuki walks in, and lights her cigarette by the barrel. She will go up in flames and die (the action is counted as an unfortunate accident)
Serving Yuki Yamazaki a poisoned fugu fish (Thrill Seeker Opportunity)
If you've decided upon this variant earlier, begin the mission with a cook outfit. If you haven't reached the necessary mastery level, visit the kitchen (M8,4) and search for an opportunity to eliminate one of the chefs. Remember that even if you have the disguise, you can still be detected by other people in the kitchen - avoid or eliminate them.
Take the kitchen knife from the kitchen and enter the pantry(M8,10). Find the fugu fish and use the knife on it - you'll receive fugu fish's poison.
Stay with the chef's outfit, and proceed to the restaurant located on the first floor. Approach the sushi table (M8,19) and press the button to prepare the meal. Add the fugu poison (you could choose a different poison, but you wouldn't complete the described Opportunity)
Stay behind the counter, and wait until Yuki appears. Once the woman approaches the table, press the right button to invite her to try out the sushi. Make sure to leave the nearest area, as Yuki will die soon after tasting the fish, and this will be seen as a major event by all people present.
Other attempts to poison Yuki
You don't have to use the fugu fish or visit the kitchen in a chef's outfit. Yuki's apartment is also a viable location - she has a bottle of water at her desk. Find a bodyguard outfit, and enter the apartment. Find the bottle (M8,7) and apply the poison.
If you want Yuki to die instantly, you can either use the fugu fish poison, or botulinum toxin. The toxin can be found in two locations - in a locked cabinet in Jason Portman's apartment (M8,5) (you'll need a crowbar) or in a rehabilitation room on level 3 of the hospital (M8,40) (distract the guards or quickly run out of the room after the theft).
If you want to eliminate Yuki in a more secluded location, you can put rat poison into the bottle. This item can be found in the corner cabinet in the kitchen (M8,9) or in the locker in 47's apartment (M8,1) (if you have a crowbar).
Yuki will make a run to the toilet once she tastes the water. Once she's up there, you can either use the fiber wire, or drown her (each action will allow you to accomplish one of the smaller challenges).
Locking Yuki up in a hot sauna
This method of elimination is recommended if you want to eliminate your target without having to acquire any additional disguises. You can complete it with the basic or ninja outfit. The sauna is located on level 1 of the hospital (M8,24), but you'll need to access the neighboring room (the one with the cold water valve), as the sauna control panel can be found there. Increase the temperature to "encourage" two patients to leave the sauna.
Wait in the same location (don't worry, you are standing before a Venetian mirror - you won't get seen) and wait until Yuki reaches the spa and decides to enter the sauna. Quickly approach the sauna door (her bodyguard will stay in the previous room) and press the button to lock them. The woman will die after a moment. If you want to hide her body, a container can be found in the room with the control panel.
Killing Yuki by approaching her in the director's outfit
This method of assassination begins with acquiring the director's outfit - I've described this situation somewhere above. Once you've acquired the disguise, find Yuki and invite her to a private talk. Then, proceed to the cable car located in the southern part of the map (M8,4). Once you've arrived to the location, listen to the conversation and wait until Yuki stands by the handrail. You can now approach her and push her off the balcony. This action shouldn't be noticed by her personal bodyguards.
Eliminating Yuki through an explosion
Before you attempt this method of elimination, you'll need to acquire a wrench. To do that, you'll have to visit the garage located on level 0 (M8,4). Additionally, you'll need to get a bodyguard outfit - eliminate the guard standing by the cable car (M8,3). Once you've got both, access Yuki's apartment and enter the balcony (M8,8). Make sure to get rid of two guards in the apartment (push them off the balcony) as they may make your job harder later. Once you've "cleared" the area, approach the gas lamp, but sabotage it ONCE Yuki returns to her apartment.
Hide on the opposite side of the balcony, and wait until Yuki stops in the neighborhood. Use a throwable item (even the wrench will do) to make her enter the balcony and stop by the gas lamp. Fire at the lamp (using a silenced weapon) to detonate the charge.
To make a sniper kill, begin the mission on the footpath in the eastern part of the map M8,17) (you'll be wearing a ninja outfit). Deliver a sniper rifle to this location. Make sure that this is a silenced model, with a scope (e.g. Sieger 300). Approach the edge of the cliff (M8,13) (the area shown on the screenshot above). Begin to look around the garden (M8,32). Kill Yuki when she stands on the small bridge (M8,25) as you'll complete an additional challenge.
Cutting off the cable car with the escaping target
This is the most troublesome variant - attempt it only if you are keen on completing all the challenges in Hokkaido.
In theory, the plan is simple. You'll need to incite the evacuation AND Yuki use the cable car located in the southern part of the map (M8,4). Before the mission begins, deliver a good assault rifle to one of the agency pick-ups (e.g. the one in the garage). Try to get access to a guard, or a bodyguard outfit along the way.
Once you've picked up the gun, get near Yuki's apartment, and wait until she appears in the area. Fire at the bodyguards guarding the main door while standing near the north-western stairs (screenshot above). If you are lucky, Yuki and rest of her entourage will leave the apartment, turn right, and attempt to reach the cable car.
Note - If the attempt is made from a different location (e.g. from the apartment area) there is a huge chance that the target will be escorted back to the hospital area. In this case, load a saved game, or wait until the alarm goes off, and everything returns back to normal.
Once Yuki and her men attempt to reach the cable car, quickly eliminate those guards that can notice and engage 47. Make sure that there aren't any guards incoming from level 1. Once you eliminate (or not) the closest targets, enter Yuki's apartment which should now be empty. Enter the balcony (M8,8) and look for the cable car. Wait patiently until the target boards the car and starts to escape - a time counter that signalizes your window of opportunity will appear.
Equip your assault rifle, or any available weapon, and start firing at the part of the mechanism that holds the gondola, shown on screenshot 1. After a few successful hits, the mechanism will be damaged enough (the time counter will disappear) and the gondola will detach after an accelerated descend, crashing on the mountainside (screenshot 2).