Itsy Bitsy Spider

I didn't see a consolidated coordinate list so I copied them from the NPC pages that had them. I have not personally checked all the locations and it may not be a complete list.
I did find Ru'murh using the pasted block below while compiling this, so it seems reasonable that you should get a hit.

Spindle appears in various quests, but he hangs out on the back of the lamp post beside Faerin Lothar in Dornogol, by the weekly quests. *Thanks MissDot
/way #2339 46.19 50.09 Spindle

Webster *Coord updated thank you Dlbert2000
/way #2255 57.06 41.75 Webster - near the Tunnel to Dornogol

Bobbin is a vendor in The Weaver's Lair, the main hub in the zone *Thank you Lornaa
/way #2255 56.4 43.2 Bobbin

A Scampering Weave-Rat group patrols around the small building on the north part of the City of Threads map to the right of the dungeon portal
/way #2213 50.2 16.0 Scampering Weave-Rat

Ru'murh
/way #2213 73.4 50.4 Ru'murh
/way #2216 45.6 51.0 Ru'murh
/way #2213 55.0 26.6 Ru'murh
/way #2213 41.6 22.4 Ru'murh
/way #2213 54.8 34.6 Ru'murh
/way #2213 79.6 56.6 Ru'murh
/way #2255 77.4 42.8 Ru'murh
/way #2255 64.2 75.2 Ru'murh
/way #2216 55.8 47.6 Ru'murh
/way #2213 78.0 53.6 Ru'murh
/way #2213 70.2 31.8 Ru'murh
/way #2213 68.6 50.8 Ru'murh

Thimble
/way #2255 55.0 68.8 Thimble
/way #2213 56.0 32.6 Thimble
/way #2255 60.6 10.6 Thimble
/way #2256 65.8 88.0 Thimble
/way #2255 53.4 53.4 Thimble
/way #2255 73.8 39.0 Thimble
/way #2255 43.8 26.6 Thimble
/way #2255 68.6 55.8 Thimble
/way #2213 26.2 51.2 Thimble
/way #2213 69.8 82.6 Thimble
/way #2213 75.2 48.6 Thimble
/way #2255 29.0 42.8 Thimble

A few things to note about this achievement:

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• Most of the coords people have listed won't actually be of any help to you. Why? Because these baby spiders (weave rats) spawn in multiple locations based on which rumor event (assuming you have unlocked said events) happens to be up. So your location and their location for any one particular weave rat will likely be entirely different. You're better off just flying around until you see a purple rumor event marker on your minimap or buying a rumor map from the faction vendor.
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• This achieve appears to be bugged (lol) in that even if you do find the desired npc, waving at them will not count towards the achievement. So it's unlikely you'll be able to complete this achievement until it's fixed by Blizz.
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• "Scampering weave rat" is actually 3 weave rats with the same name running around a fairly large area. Just go to /way 46.95 15.27 (within the City of Threads zone) and wait until their patrol comes around to you. Or use a /tar macro and fly around in that area until you get a hit.
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• People commenting here have not clarified whether the coords they're posting is within the City of Threads map (which is a sub-zone contained within Azj-Kahet) or not. So if you just randomly plug their coords into TomTom, then there's a good chance you're gonna be sent on a wild goose chase into oblivion if you're in the wrong zone at the time.
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• The only Spindle that would count towards the achievement for me was the Spindle that is part of the one-time quest Saving Private Spindle (ID: 226019). Just unlock his cage and /wave at him before you accept his follow up quest. So I had to do it on an alt.
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• It is unknown where Swift is. Nobody seems to have been able to find him as yet.
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Edit: Blizz changed 2 of the requirements of this achieve. It appears that Swift has been replaced by [npc=224734] and the General has been removed.

Some of these you may have to repeat quests with an alt to tick off if you've already completed the related quest.
The ones that count towards the achievement found so far:

/way 39.4 65.4 Webster (near raid entrance)
/way 47.67 15.64 Scampering Weave-Rat
/way 56.04 32.89 Thimble
/way #2213 87.78 59.28 Spindle (during the Saving Private Spindle quest)
/way 64.15 74.30 General's Scouting Shadecaster (during the A Spider's Eye View quest)