Slum It in the Summit

Ok- I cannot remember exactly where I started all the questlines for this achievement but with some research I think I can provide a close guide that will at least put you in the right place, if not actually on the quest lines. I've also listed the correct names of the criteria as it is in WoW. I hope this helps..

Westwind Rest - starts with Admiral Taylor(71.6,93) near Binan Village, south-east corner of Kun-Lai Summit.
Inkgill Mere - starts with Merchant Shi(74.8,88.8) near Binan Village, south-east corner of Kun-Lai Summit.
The Burlap Trail - starts with Brother Lintpocket(58,61.4) near One Keg, just south-east of the center of Kun-Lai Summit.
The Thunder King - starts with The Curious Text(57.2,47.9), in the Valley of Emperors, south of Mogushan Terrace.
Zouchin Village - same as The Thunder King
The Yaungol Invasion - starts with Farmhand Bo(53.8,84) near Westwind Rest, in the south of Kun-Lai Summit
The Yak Wash - starts with Muskpaw Jr(75,74.6), south-east of The Yaungol Advance on the east coast of Kun-Lai Summit
Kota Peak - this one I'm really not sure about, but I think it starts with Brother Trailscenter(51.6,67.8) on The Burlap Trail, halfway between One Keg and Kota Basecamp.
Temple of the White Tiger - starts with Wanderer Chu(72,94.2), south of Binan Village or Farmhand Bo(53.8,84) near Westwind Rest in the south of Kun-Lai Summit.
The Shado-Pan - starts with Admiral Taylor(71.6,93) near Binan Village, south-east corner of Kun-Lai Summit.

From what I can tell - the list they put for the criteria isn't exactly wrong, it's just the names of actual quests that are apart of the specific quest lines. For example, 'Stealing Their Thunder King' is actually the fourth quest in the series, same with 'Back in the Yak'.. If you click on their criteria and then look on the right hand side to see the whole questline, then click on the first one and go there you will probably be in the right place.

The Road to Kun-lai Quest Tree From Whiterock

#)Robbing Robbers of Robbers #)Educating Saurok #)The Spring Drifter(The Veiled Stair)

#)The Road to Kun-Lai{H}(Multiple zones)

+)Hit Medicine +)All of the Arrows +)Call Out Their Leader
 ├─────┬────────┴───────────────────┘         |
 |     |                                    Turnabout*
 | The Defense of Shado-Pan Fallback*
 |
 ├──────────────────────────────────────┐
a)Admiral Taylor has Awakened(A,v2,v3) a)General Nazgrim has Awakened(H,v2,v3)
b)Westwind Rest(A)                     b)Eastwind Rest(H)
 |                   ┌──────────────────┘
b)Challenge Accepted{H}
 | |                 └───────────┬>c)Blue Dwarf Needs Food Badly(A)
 | ├>c)Round 'Em Up{H}           ├>c)Best Meals Anywhere!(H)
 | └>d)Profiting off of the Past └>d)Deanimate the Reanimated{H}
 |
 ├───────────────────────────┐
d)Mogu? Oh No-gu!{H}    e)Trouble on the Farmstead{H}
 |                        /     \
 |       e)Farmhand Freedom     e)... and the Pot, Too! 
 |                       └─┬───┬─┘
 | e)Back to Westwind Rest(A) e)Back to Eastwind Rest(H)
 ├─────────────────────────┴───┴─┬───────────────────┐
 |                               |                   |
f)In Tents Channeling{H}        f)Barrels of Fun{H} f)Pandaren Prisoners{H}
f)The Ordo Warbringer{A2,H1,H2}  |                   |
 |                           └─┬─┴─────────────────┬─┘
Muskpaw Ranch{H}*              ├>The Shado-Pan{H}* ├>The Missing Merchant{H}*
                               └>Beyond the Wall*  └>Cho's Missive{H}*
Legend:
+ means Can start anytime, prequests not needed.
# means Other Zones
(A)/(H) means Alliance/Horde only.
{H} means Quest Have Horde Variant, click {H} for it.
* means another Quest Tree.

Additionall info:

1. 
   
2. Yes, Shado-pan questline have such weird prequests :D
3. 
   
4. Awakened quests have 3 version of quests each starting from NPC that gave you previous quests.
5. 
   
6. Ordo Warbringer have quest that starts via pop-up after Channelers and backup from Taylor/Nazgrim if you abandon first.
7. 
   

If you're missing the Yak Wash line, check the quests Yakity Yak and The Late Mrs Muskpaw.