This list is from my old PS guide from 2001. That list was color-coded in 5 colors but that's not possible here. It's also why the headings contains the CD1, CD2 and CD3.
I'm currently transforming my old list into this new guide. Some extra notes were added/taken from FF Wikia's ATE[finalfantasy.wikia.com]but most are my own.

ATEs in bold text are mandatory (often forced) and usually not missable. The text is grey in the game.
ATEs in normal text are non-mandatory and missable (because you don't want to do them or they didn't get triggered because you watched them in the wrong order or missed a step/conversation earlier in the game). The text is blue in the game.
Text in italic are instructions or extra info.
Example:
ATE's name - City / trigger area: people involved trigger instructions for the next ATE (extra info)

Some ATEs may be triggered in other places or orders than what my guide shows, if you follow my list they should all get triggered without missing an ATE.

At least two ATEs have special options within the ATEs so depending on how you choose you'll miss a little bit of the story or get a different dialogue or scene. Just re-play the whole game or re-load a previous save to see what happens with the other choice.
Beware that some ATEs won't trigger if certain conditions aren't met; like watching an ATE in the wrong order or area, or by picking the wrong answer or conversation when you get a choice. These things will almost always be pointed out in the guide.

Mogster's three tutorial ATEs don't count towards the achievement.
You need to watch all the ATEs in the same playthrough. Reloading an earlier save to watch a missed ATE doesn't really count if you then continue to play from your last save.

-----
23/4 2016: started to update each area as I play (currently in Treno on CD3; card playing).

6/5 2016: added a sort of walkthrough to each CD title, so you can see when the ATEs are about to show up (marked in bold). Not every side area is mentioned, just enough to know where you are and where to go next to get the story moving.

17/6 2016: still in Treno (the tournament).

29/8 2021: I'm finally playing this game again and updating this guide.

Prima Vista Airship, Alexandria, Alexandria Castle, Evil Forest, Mist Continent - Gunitas Basin / Melda Plains, Ice Cavern, Mist Continent - Norlich Heights (South Gate, Observatory Mountain), Village of Dali, Cargo Airship, Lindblum Grand Castle (Castle, Business District, Industrial District, Theatre District, Base Gate), Mist Continent - Eunoros Plains / King Ed Plains (Chocobo's Forest, Bodhen Arch), Qu's Marsh, Gizamaluke's Grotto, Grand Citadel South Gate (Bodhen Arch), Mist Continent - Daines-horse Basin (Burmecia Arch), Burmecia: Realm of Eternal Rain

• The Forest Keeper - Prima Vista / Crash Site (Mosco the Moogle): Garnet & Vivi
  
• Time To Escape - Prima Vista / Hallway: Steiner's room
  
• Girl Who Was Left Behind - Prima Vista / Hallway: Ruby in Alexandria's bar
  
• My Little Baby (must watch Time To Escape) - Prima Vista / Hallway: Cinna's outside the ship
  
• Orchestra In The Forest - Evil Forest / Trail: The Tantalus Orchestra in Prima Vista
  
• Do As I Say, Not As I Do - Evil Forest / Spring: Baku & Blank in Prima Vista
  
  
• Teach Me, Mogster! Lesson 1 - Gunitas Basin (in the camp after exiting the Evil Forest): Mogster & Moggy in Qu's Marsh
  
• Teach Me, Mogster! Lesson 2 - Ice Cavern / Cave: Mogster & Moggy in Qu's Marsh

----------
After Watching Girl Who Was Left Behind, you should talk to Mosco. He gives Zidane a letter from Ruby. I'm not sure but I think you can only get the letter if you watch the ATE (that's when I got it).

The Orchestra ATE plays music from Final Fantasy VII.

• Vivi, Confused - Dali / Inn: Vivi's outside the inn
  
• Dagger Tries - Dali / Inn: Dagger's in the field
  
• Cat's Eye - Dali / Village Road: Vivi's near the windmill
  
• Cat's Eye 2 - Dali / Village Road: Innkeeper
  
• Dagger Tries Harder - Dali / Village Road: Dagger's in the shop
  
• Queen Brahne's Steiner - Dali / Inn: Steiner's in the pub

----------
Dagger Tries Harder can be triggered in three ways:

1. Visit the area Field and then three more areas.
   
2. Watch Dagger Tries at the inn, visit three areas and then view the inside of the inn from the top (window looking in).
   
3. Explored enough areas to trigger.

Queen Brahne's Steiner triggers after watching Dagger Tries Harder, having talked to Dagger in the weapon shop and watched Vivi in Cat's Eye.

• Teach Me, Mogster! (My First Synthesis Lesson) - Lindblum / Inn: Mogster & Moggy in Qu's Marsh
  
  
• Small-Town Knight In A Big City - Lindblum / Main street (Business District): Steiner is lost
  
• Vivi's Shopping - Lindblum / Main street (enter the B.D. Station): Vivi's shopping (reward: Kupo Nut)
  
• Steam Engine - Lindblum / Station Area (Theater District): Steiner is still lost (near the docks)
  
• What Can I Do? - Lindblum / Hideout (Theatre District): Dagger at the castle (after Zidane leaves Tantalus' hideout)
  
• Baku And His Crew - Lindblum / Theatre Avenue: Baku & Co at South Gate / Bodhen Arch

----------
Don't forget to pick up Quina in Qu's Marsh after leaving Lindblum, s/he's needed for future ATEs.

Summit Station, South Gate - North Station, Mist Continent - Bentini Heights (Dali Arch, Dali, Treno Arch), Dark City Treno, Gargan Roo, Mist Continent - Daines-horse Basin, Cleyra's Trunk, Cleyra Settlement, Alexandria Castle, Pinnacle Rocks, Lindblum, Qu's Marsh - Excavation Site, Fossil Roo, Outer Continent - Donna Plains (Qu's Marsh), Conde Petie, Black Mage Village, Conde Petie, Mountain Path, Madain Sari, Iifa Tree, Madain Sari, Iifa Tree

• Treno Tradition - Treno / Gate: Dagger on the Walkway follow Dagger's path, go left
  
• Pursuit - Treno / Walkway: Dagger near the Bishop's House follow Dagger's path
  
• Confusion - Treno / Bishop's House: Dagger near the Knight's House follow Dagger's path, down to the right (see below)
  
• Unexpected Visitor - Treno / Card Stadium: Dagger in the Auction House go up the stairs to the right
  
• Ambition - Treno / Knight's House: Marcus and the street kids Natalie & Mario go up the tower/stairs to the right and then down
  
• Meeting Place - Treno / Slum: Marcus & Baku in Treno's Pub (go pick up Dagger afterwards to continue)
  
• Crime And Punishment - Treno / Walkway: Cinna & Baku at the Summit Station (take the stairs back into town from Tot's Residence instead of going down the manhole)

----------
During Treno Tradition: Garnet is pick-pocketed by the Four-Armed Man. The player may press the X button to reduce the amount stolen to 500 Gil instead of 1,000 Gil when the "!" icon appears. (text taken from the FF Wikia). Dagger just stands there if he steals 1,000 Gil but chases after him if she notices.

After Pursuit & Confusion: as Steiner, enter the Bishop's house (the actual house to the left leading to the Synthesist) and confront the thief to get a Power Belt. He's leaving as you're entering so be quick about it (remember he entered the house during Pursuit).

Crime And Punishment might also trigger after going down the manhole into Gargan Roo, instead of back out into Treno.

---
Walkway = Tot's Residence
Bishop's House = Synthesist
Knight's House = Fighting Arena & Weapon Shop
King's House = Auction House & likely Kuja's Residence
Queen's House = Stella Stellazzio

• No Yummie-Yummies! - Cleyra / Town Area: Quina at the Observation Point
  
• There A Mushroom! - Cleyra / Observation Point: Quina near the Water Mill (Zidane can now find Quina at the sandpit)
  
• Don't Hate Me - Cleyra / Water Mill Area: Vivi in the Town Area
  
• I-I Haven't Hurt Anyone - Cleyra / Water Mill Area: Vivi in the inn (Zidane can now find Vivi there)

----------
Don't Hate Me can be triggered in these areas: Water Mill Area, Windmill Area, Observation Point and Cathedral.
I-I Haven't Hurt Anyone can be triggered in these areas: Observation Point, Water Mill Area, Windmill Area and Cathedral. Dan and his family outside the Inn changes what they say after watching this ATE.

No Yummie-Yummies! can be triggered in these areas: Town Area, Water Mill Area, Windmill Area and Cathedral.
There A Mushroom! can be triggered in these areas: Entrance, Observation Point, Windmill Area and Cathedral (also in the Inn after talking to Vivi).

• Friendship - Alexandria Castle / Chapel: Marcus in the Evil Forest

----------
Failing to defeat Zorn & Thorn before the countdown reaches 00:00 will trigger a game over (tested & confirmed by Aroth).

• The Third Jewel - Lindblum / Shopping Area (Business District): Alexandrian soldiers in Lindblum's castle (after meeting Cid, go explore)
  
• Brahne's Fleet Arrives - Lindblum / Shopping Area (Square in B.D.): Lindblum soldiers on a ship (talk to the waiting man)
  
• (Gwok-gwok!) How Infuriating! - Lindblum / Base Level: Alexandrian soldiers at Serpent's Gate

----------
Pick up Quina in Qu's Marsh again.

• Vivi And The Couple - Conde Petie / Corridor: Vivi's outside the inn go left (to the pathway)
  
• Quina Accused - Conde Petie / Pathway: Quina in the item shop go left (to the inn)
  
• Quina Can't Communicate - Conde Petie / Inn: Quina at the weapon stall go right, then up
  
• Dagger And William - Conde Petie / Shrine: Dagger at the inn
  
• Hungry Bryan - Conde Petie / Shrine: A "pyntie-het" is coming (after talking to Vivi)

----------
If you enter the Item Shop without first watching Quina Accused, you'll miss it. It's to the right of the Corridor.
If you go to the right in the Item Shop without first watching Quina Can't Communicate, you'll miss it.
If you go upstairs without first watching Vivi And The Couple, you'll miss it.
If you watch Hungry Bryan (triggered by talking to Vivi) without first watching Dagger And William, you'll miss it. The same will happen if you haven't yet watched any of Quina's ATEs.

• Everyday Life - Mage Village / Entrance: Black Mage No.163 in his shop upper right path (by the shop)
  
• Life On The Run - Mage Village / Item Shop: Vivi & Dagger left door twice (through the shop)
  
• Gourmand's Nose - Mage Village / Pond: Quina by the water mill & stable lower right path, right (to the stable)
  
• Different Language - Mage Village / Water Mill: Vivi and Black Mages No.288 & No.56 at the cemetery go down, upper left, left (pass the shops to the cemetary, see Vivi)
  
• Visitor, Not Invader/Intruder - Mage Village / Cemetery: Dagger and Black Mages No.192 & No.32 in the synthesis right, up (to the synthesis, meet Dagger)
  
• Life Cycle - Mage Village / Synthesis: Quina and Black Mages No.111 & No.33 in the stable

----------
If you take the lower right path instead of the upper right path from the entrance, you'll miss Gourmand's Nose so pay attention to where the paths are.

---

1. After you enter the village for the first time, at the entrance of the village watch the "Everyday Life" ATE.
   
2. Then take the upper right path towards the inn and watch the "Life On The Run" ATE in this screen.
   
3. Go through the door on your left into the item shop and exit via the other door to the left, you should be in front of the item shop and synth shop at this point. In this screen, watch the "Gourmand's Nose" ATE.
   
4. Go back to the beginning and take the lower right path towards the chocobo stable where the moogle is. Watch the "Different Language" ATE here.
   
5. Go to the cemetery to the left of the synth shop and watch the "Visitor, Not Invader" ATE there.
   
6. Go inside the synth shop now and after the cutscene, watch the "Life Cycle" ATE.
   (explanation by Cress)

• Nuptial Joy - Conde Petie / Shrine: Vivi and Quina

----------
After Zidane and Dagger's ceremony in the shrine, answer "Why don't you guys get married, too?" when Vivi and Quina wonders what to do.

• Vivi's Feelings - Madain Sari / Open Area: Vivi at the left path upper right path
  
• Dagger's Feelings - Madain Sari / Path (right): Dagger at the entrance go back left
  
• Eiko's Feelings - Madain Sari / Open Area: Eiko in the kitchen go left (try to enter the kitchen, follow Morrison)
  
• Eiko's Kitchen - Madain Sari / Open Area: Eiko in the kitchen (follow Morrison)
  
• Eiko's Kitchen 2 - Madain Sari / Open Area: Eiko and Quina in the kitchen (se below)

----------
To make a good dinner:
Try this in Eiko's Feelings: send Chimomo fishing, ask Mocha to dig up potatoes and let Momatose help out in the kitchen.
Try this in Eiko's Kitchen: prepare a meal for 11 or 12 people, leave out the Oglop ingredient, let Momatose cook and go help with the fishing.
Try this in Eiko's Kitchen 2: ask Quina for advice.

You can find Quina by talking to the moogle blocking the way to the Eidolon Wall (after watching Dagger's Feelings). If Eiko helps with the fishing (in Eiko's Kitchen), Quina will show up again.

Load a previous save and try other cooking combinations and see what happens. E.g. Cook for 5 people and add an Oglop, ask Chimono to help in the kitchen and send Momatose to go fish, don't have Eiko help with the fishing etc.

The choices in Eiko's ATEs affects the dinner scene and possibly the future ATE I Forgot!.

Alexandria, Treno (Quan's Dwelling), Alexandria Castle, Lindblum (Castle, Business District, Theatre District), Blue Narciss Airship (revisit areas and finish sidequests), Black Mage Village, Forgotten Continent - Blairsurpass Plains (Qu's Marsh), Oielvert, Desert Palace, Lost Continent, Esto Gaza, Mount Gulug, Lindblum / Alexandria, Hilda Garde 3 Airship, Alexandria, Daguerro, Ipsen's Castle, Four Shrines (Forgotten Continent: Water, N Lost Continent: Fire, SE Forgotten Continent: Wind, E Outer Continent: Earth), Hilda Garde 3 Airship (last chance to finish sidequests and visit areas), Shimmering Island to Terra, Bran Bal, Pandemonium

• It's So Big - Alexandria / Main Street (right of the pub): Eiko and three chefs at the castle entrance
  
• Long Time No See! - Alexandria / Main Street (left of the pub): Three Nero Brothers
  
• To Fly High - Alexandria / Square: Blank and Marcus in the alley
  
• Artemicion - Alexandria / Square: Artemicion and Stiltzkin in the steeple
  
• I Forgot! - Alexandria / Main Street: Baku at Ruby's theatre (after Vivi joins up with Zidane again)
  
• Clowns On A Dark Night - Alexandria / ?: Thorn & Zorn and Blank & Marcus

----------
The choices in Eiko's kitchen (several previous ATEs in Madain Sari) possibly affects the ATE I Forgot! (unconfirmed and atm unknown how).

• Eiko Talks Life - Treno / Tot's Residence: Eiko & Vivi on the Walkway
  
• How He Ended Up Here - Treno / Tot's Residence (stairs): Vivi & Marco at the Gate
  
  Treno / Tot's Residence (stairs):two choices for Vivi
  
  1. Stop by at home: Home Sweet Home (Vivi talks about his past)
     
  2. Stay in Treno: Hippo's Prize (card tournament challenger)
  
  
• *Hippo's Prize - Treno / Walkway: Hippo, Mario & Natalie and Vivi (see Vivi's choice 2)
  
• Memories By The Water - Treno / Walkway, Gate or Bishop's House : Amarant & Eiko, Four-armed man outside Queen's House
  
• City People - Treno / Card Stadium: Eiko & Quina, Four-armed man inside Bishop's House (must watch Memories By The Water, reward: Chimera Armlet)
  
• *Home Sweet Home - Treno / Card Stadium: Vivi in Quan's Dwelling (see Vivi's choice 1, after Zidane's first card match)
  
• Good Old Days - Treno / Bishop's or Knight's House: Freya & Amarant outside the Auction (after Zidane's first card match)
  
  Treno / Bishop's or Knight's House: two choices for Freya
  
  1. Of course I'm interested: Lessons of Life (Amarant talks about his past)
     
  2. I won't force it out of you (resulting in a missed ATE)
  
  
• Lessons of Life - Treno / Bishop's or Knight's House: Freya & Amarant, Zidane outside the Auction (see Freya's choice 1)
  
• Hallucination - Treno / Card Stadium: Quina outside the weapon shop (after Zidane's second card match)
  
• Premonition - Treno / Knight's House: Eiko & Tot (after Zidane's second card match)

----------
Either one of Vivi's ATEs count towards the achievement, i.e. you don't need to watch them both (reload a save or start a new game to see the other ATE if you want to).

• If Vivi stays in Treno, your second opponent in the Card Tournament will be Mario the street kid. He has the rare Namingway Card.
  
• If Vivi visits Quan's Dwelling, you can go and talk to him and learn more about his origins. If you do this before winning your first card match in the Tournament, the ATE Home Sweet Home will not trigger. It's better to go and talk to Vivi after watching the ATE since he'll join you.

Lindblum Castle / Guest Room: two choices for Zidane

1. "Where's Dagger?" (find Dagger near the telescope)
   
2. "How did I get here?" (find Cid in the Royal Chamber, miss a future ATE)

• Something Washed Ashore - Lindblum / Hallway: Soldiers and Quina at the harbor (must watch Hallucination)
  
• *My Bad/Fault - Lindblum Castle / Telescope: Blank in the Hall (only if Zidane first ask Blank about Dagger and then don't talk to him again)
  
• Self-reproach - Lindblum Castle / Conference Room: Dagger at the telescope (while Zidane's talking to Regent Cid)
  
• Deep Anger - Lindblum Castle / Conference Room: Kuja and Zorn & Thorn on Hilda Garde 1 (while Zidane's talking to Regent Cid)
  
• My Hammer - Lindblum Castle / Hall: Cinna, Marcus and the Nero brothers at the Tantalus Hideout
  
• The Rally - Lindblum / Station Area (Theatre District): Freya and Burmecian soldiers at the castle (Zidane talking to Kal and Wei)
  
• No Free Lunch - Lindblum Castle / Hall: Quina in the Shopping Area (just after talking to Cid in the Conference room) go to Business District before going to the Blue Narciss
  
• Give Me My Money - Lindblum / Harbor (Blue Narciss): Baku in the Shopping area (must watch No Free Lunch and be broke)

---------
My Bad/Fault: Go left after exiting the guest room. Go down to the lift, pick the Upper Level. Exit the lift. Take the left stairs going up, continue going up until you find Dagger. The key to triggering Blank's scene is for Zidane to not talk to Blank again. If you want Blank to get angry at you, talk to the soldiers while looking for Dagger. Some of them mention Cid and the Royal Chamber.

No Free Lunch: Pick up Quina in the Business District but make sure you have less than 50 gil. Make sure you spend your gil while looking for the three potions.

Team
Recovery

Place To Call Home
Where The Heart Is
Came Into This World
The Truth

The Lift both groups work together

---------
1) Change the standard heading of the elevator to 0 (zero).
2) Check all three possibly entrances to the elevator, only to get knocked back by a forcefield.
3) Change the standard heading of the elevator to 2 (two).
4) Repeat Step 2.
5) Return to the elevator room and the ATE will be activated.
(explanation by Cress)

Black Mage Village, Invincible Airship (Treno, Alexandria, Lindblum, BMV), Iifa Tree, Memoria