Syberia 3

This achievement is missable. It is the final puzzle in the game. It is a smoke signal puzzle. To unlock the achievement, Kate must solve the puzzle without allowing the fire that makes the smoke to go out.

The furnace where you must solve the smoke signal puzzle is to the right of the guard house.  Before solving it, you must cross the bridge to get some instructions from the Youkol Watcher on the other side.  The guard in the guard shack will lower the bridge when Kate talks to him.  Caution:  In order to get the below achievement, you must lower the water before approaching the guard.  To do so, go to the right of the guard shack, go down a ladder and pull a lever on the lower level.  After you have lowered the water, talk to the guard.  Although a little slow on the uptake, Kate manages to convince him to take a bribe.  He mentions that the water needs to be lowered and is a little taken aback when Kate tells him she has already taken care of it.  This will unlock:

Position Kate near the bridge and the guard will lower it.  Kate crosses to the other side and talks to the Youkol Watcher in a small fenced in area.  He says that for the Youkol migration to proceed, the spirits will need vodka and a special smoke message.  Kate returns across the bridge triggering a cut scene that shows the guard departing.

Kate will need several items—brick, Shaman stick, knife, lighter, vodka, & papers.  The order in which she gets them is unimportant.  This guide begins with the brick.  So, examine the tire treads the departing motor bike left behind and Kate will pick up a brick that had been used as a wedge for the tire. 

Going to the Caravan, Kate enters the first Yurt with a ladder.  This is the Shaman’s Yurt.  The Shaman will provide a little more cryptic info about the smoke signals before nodding off.  Pick up the Shaman’s staff inside a case.  Exit the Shaman's Yurt and continue deeper into the Caravan.  Enter the second Yurt with a ladder, this is Kate’s Yurt.  Pick up the lighter and a knife from a box that contains some of Kate’s belongings.

Return to the Guard Shack.  Go to the right and behind.  Kate uses the brick to open the door.  Inside the first room pick up the guardman’s flask.  If you look at it in inventory, you confirm it contains vodka.  Inside the second room, pick up some old custom forms.

Go outside and down the ladder you used to lower the water.  Go into the room and press a button.  This causes a basket to come across a cable from the other side.  Place the vodka in the basket and press the red button again.  The basket will go back and return with a couple of sacks of sawdust.  Pick them up.  Go back up the ladder.

You are now ready to solve the smoke signal puzzle.  The below video begins at this point and shows how it is done:


This is a summary of the steps that are shown in more detail in the video:
1.  Get two resins from the left chimney and a resin from the second chimney from the right.  While you are at it, position the bottom cranks so they are vertical.  It is important, after you light the fire, to have at least one crank vertical at all times. 
2.  Open the lower part.  From the left side, take two resins and three numbered funnels.  Note that one is a full piece whereas all the others have been quadrant shaped wedges.
CAUTION:  You will now light the fire.  If, at any point, after lighting the fire, you interrupt the smoke coming out of the furnace, you will void the achievement.  If that happens, immediately press and go to the main menu.  Choose continue and you will be at the checkpoint before the puzzle started.
3.  Place the log in the lower center.  Place the guard shack papers (old custom forms) in with the log.  Use the lighter to light the papers.  Making sure that you have at least one chimney crank in the vertical position, look to the left of the furnace and turn the valve there to a vertical position.  This is an exhaust valve.  Turning it vertical sends all the smoke to the four chimneys.  If all chimney cranks had been horizontal, turning the valve shut (i.e., in the vertical position) would void the achievement.
4.  Go to the other side of the circular area to a chopping block.  Place the big blue resin on it and use the Knife.  This will cut a wedge a quarter of the size of the big chunk.
5.  Return to the furnace.  Place the Shaman’s staff on the top center.  Note the symbols—their shapes and their color.  From left to right, you will see red, blue, blue, and yellow symbols.  You will be placing the resin in the chimneys in the same sequence—left to right: red, blue, blue, and yellow.
6.  For each chimney:  Make sure the bottom crank is vertical.  Raise the top platform to see where the hole in the bottom is.  If necessary, use the handle on the left to make sure that you will have a grate and not a hole above the bottom hole.  Lower the top platform.  Place the resin (quarter-size of the appropriate color) on the quadrant of the grate just above the bottom hole.  Close the chimney.
7.  Zoom out.  You will see that one of the chimneys does not have smoke coming from it.  Change the point of view to the back.  Take out the funnel from the open chimney.  The shapes of the funnels correspond to the symbols on the staff that you had just looked at.  When looking from the front, the red shape was on the left and corresponded to funnel #1.  Since we are in the back, we must put funnel #1 in the chimney on the far right.  Open it, place the funnel in and close the chimney.
8.  Place funnel #2 in the chimney next to where you put funnel #1.  CLOSE the chimney.  Then place funnel #3 in the chimney to the left of the chimney with funnel #2 and close it.  This is the chimney that mistakenly contained funnel #2.  Finally, place funnel #4 in the far left chimney and close it.  When you close the last chimney, the achievement will unlock.