(before you say anything, I’m the same author as this this post, But I lost my account, in fact, I’d thank the admins if you delete the previous post to avoid confusion)
Torren
Telnor Town
Delta Bulbasaur, Charmander or Squirtle: Starter Pokemon
Delta Bulbasaur, Charmander or Squirtle: (Post Elite Four) battle Professor Sylvan.
Telnor Cave
Delta Diglett: Use Relic Song in front of the music pattern on the underground level, Delta Diglett will spawn in front of the stairs that lead to the exit in the underground level. Once you interact with it, it will trigger a fight.
Route 1
Delta Dwebble (Cake): Near the entrance to the Dark Cave there’s a Hiker that will trade you a Delta Dwebble in exchange for a Totodile (Totodile can be found in the Grass in Route 2).
Ancient Ruins
Delta Geodude: Use Tesseract, Delta geodude will be in front of the ruins. Once you interact with it, it will trigger a fight.
Suntouched City
Delta Aipom: Agree to help the man in the western side of the city, meet him in the garden in the upper part of the city, he will tell you that you need honey (Honey can be obtained in route 3, at the end of a somewhat hidden path behind some trees southeast of the house on the hill. Requires Surf). Give the honey to the man, and that will trigger a fight against Delta Aipom.
Broadcast Tower Missions
Delta Grimer: Mission 2 (Availible after completeing Mission 1 and travelling a random number of steps)
Delta Solosis: Mission 4 (Availible after completing all previous Missions, Defeating the Selene Gym and travelling a random number of steps)
Route 3
Delta Scyther: In the house on the hill there’s a Hiker that will trade you a Delta Scyther in exchange for any Steel-type Pokémon.
Metchi Town
Delta Ditto: After doing Delta Noibat’s sidequest, talk to the scientist in Gaea town, then go back to Metchi town and meet him in the daycare. When he asks you for a Pokemon, type “Ditto” and then he will let you in. Explore the daycare until you find Delta Ditto, fight it and capture it.
Route 4
Delta Sunkern: Interact with it in the Hidden Grotto (12.5% chance of spawning) and fight it.
Delta Ralts: Is taking refuge inside of a house in the northeastern corner of the map, along the river. Interact with it and fight.
Vipik City
Delta Wooper: Below the Pokemon center, there’s a girl that tells you that she puts candy inside the creepy stump just above her and during the night something eats the candy. You must put an acceptable candy in there (There’s a full list on the wiki, but some examples of acceptable candy are Rare Candies, Honey and Lava Cookies), and interact with the stump during the night (Between 12:00 AM and 5:59 AM). This will trigger an encounter with Delta Wooper.
Samsara Cave
Delta Pidgey: Use Surf and go to the northern side of the cave, enter the room and go to the part with all the pidgeotto statues. The statue in the middle of the left side has a switch, flip it and a stair will appear. Go downstairs, interact with delta Pidgey and fight.
Roggan Town
Delta Emolga: (Post 7th gym) Interact with a man in the Pokemon center, it will give you a bycicle. After the 7th badge has been obtained, interact with it again and it will give you a Delta Emolga
Battle frontier (Requires Rock Climb)
Delta Plusle: There’s a hiker that will trade you a Delta Plusle for a Regular Minum (Minum can be found in the Grass in Route 6).
Delta Minum: There’s a hiker that will trade you a Delta Minum for a regular Plusle (Plusle can be found in the Grass in Route 6).
Delta Golett: Reward for winning the Tube Challenge
Helios City
Delta Lotad: A Firebreather on the second floor of the rightmost of three houses in a row, just north of the park area is willing to trade his Delta Lotad for any Dragon-type Pokémon.
Helios Sewers
Delta Heatmor: Use Heart Swap in the bottom right corner of the map to swap places with the Manaphy statue on the other side of the wall. Then Surf towards the north. Interact and fight with the delta Heatmor.
Utira Library
Delta Budew: Hidden within a secret room in the Far West Wing’s northernmost bookcase. The room is revealed by interacting with one of the books to the left of the boy staring at the bookcase.
Route 8
Delta Munchlax: Interact with it in the Hidden Grotto (25% chance of spawning) and fight it.
Miara Town
Delta Koffing: A girl in the trading center will trade you a Delta Koffing in exchange for a Pseudo legendary, or one of it preevolutions. Here’s how you can gain relatively early access to one: after gaining access to Anastasia’s Lab, turn a Rotom (which you can get by inteacting with any TV on any town) in your team into Heat Form. A hiker inside a house will trade you that for a Beldum, then return to the trading center and trade it for Delta Koffing.
Delta Axew: Agree to help the Sailor in the southwestern part of the town (requires Surf), clear the trade outpost, interact with the Axew behind the Bossman Derrick, fight it and capture it.
Stormy Seas
Delta Dunsparce: On the southwestern border of the map there’s a very small diving spot. Dive there, go north to the other room, then go south and use Dive again. Delta dunsparce is hiding behind a tree in the northern side of the island. Find it, fight it and capture it.
Whirl Islands
Delta Clamperl: Can be encountered by using Dive in the dark patch of water found to the right of the northeasternmost island.
Route 9
Delta Combee: Interact with it in the Hidden Grotto (12.5% chance of spawning) and fight it.
Sonata Hills
Delta Litwick: Go through the backwoods of the building, and enter the building through the back entrance. You will find a hungry Delta Litwick inside. Give it an Oran Berry and it will instantly join you, no fight required. (If you don’t have any Oran Berries, you can win some with the sonata tracks, being sponsored by Vileplume Berry Harvest)
Nasca Town
Delta Pawniard: Use Dive on a small spot in the northwestern pond, exit and go north, to the Power Farm. Interact and fight with Delta Pawniard There.
Murk Forest
Delta Scraggy: Interact with it in the Hidden Grotto (12.5% chance of spawning) and fight it.
Delta Metang (Spider): Agree to help the Hiker in Hekate town, go where he indicates you and battle all 6 Ariados that appear (You will need Heart Swap to reach the sixth one), then fight the Delta Metang that appears on the center of the area.
Delta Shinx: Use Surf in the northwestern lake and go to a somewhat hidden path, then go north and use some Strength replacement, then keep going north. Enter the next room and you will see a house. To the left of the house you will see a passage similar to a hidden grotto, enter and you will see a Delta Shinx, fight it and capture it.
Fiery Caverns
Delta Snorunt: Can be encountered by using Tesseract in the area with the third boulder and then following the path northwestward.
Selene City
Delta Liepard: After interacting with several NPCs (the old man in the Pokémon Center and answer “no” to his question, the man in the house next to the Cresselia statue, the person next to the PikaTaxi, the boy that appears next to the gym and the girl in the house to the right of the Pokémon Center) then interact with the shadow next to the pokemon center, and you will be able to fight it. I think it only appears at night.
Ancient Tower (Dive in the pond in the center of the Selene City)
Delta Noibat: Use Tesseract and move quickly between the broken platforms (Free advices: use your bike to avoid falling and be sure to read ALL the notes in the tower to unlock the Delta Ditto Sidequest), then take the egg (I think you need a free spot in your team or else it won’t give you the egg, but I’m not sure) and leave.
Dragon Ruins
Delta Bergmite: Use Tesseract at the southeast spot of the central altar. Fight the Delta Bermite that appeared. Beware: it can know roar, so something like a quick ball could be useful.
Route 15
Delta Cyndaquil: There’s a Satellite tower right in the center of the route. On the left of the tower there’s a cientist that will ask the player for help of fixing something that’s wrong inside the tower. Once you accept, you can go inside of the tower. There are 3 floors, each one with a puzzle harder than the last one. once you complete all 3, you can fight the pokemon inside the fourth floor.
Amphitrite City
Delta Shuckle: A Black Belt located to the east of the Amphitrite Gym offers to trade the player his Delta Shuckle for a Bulbasaur (You can get a Bulbasaur in the Hidden Grotto of Route 14, with a 12.5% chance of spawning, or from the old man that asks you to return his old photo on Nasca town).
Mt. Rose
Delta Phantump: Interact with it in the Hidden Grotto of the lower part of the mountain (there are 2 Hidden Grottos, one at the lower part and one on the top) (it has a 25% chance of spawning) and fight it.
Deyraan Town
Delta Misdreavus: First interact with the girl and the boy that are making “Snowmons” to the left of the house near the center of the town. Then search the town for another snowmon, interact with it and return to the girl. Then run around town, fining the new Snowmons, interacting with each one, until you find the Misdreavus making a Snowmon of itself, interact with it and fight.
Route 16
Delta Girafarig: A woman in the house to the north is willing to trade the player a Delta Girafarig in exchange for any fully evolved Pokémon that knows Frenzy Plant, Blast Burn, or Hydro Cannon. Those are only Starters. You can get a fully evolved Venusaur in the tall grass on the south of Narra Town (10% chance of spawning), and the lady in the northwesternmost house of Nasca Town can teach any starter Pokémon Frenzy Plant, Blast Burn or Hydro Cannon.
Narra Town
Delta Growlithe: A man in the southwestern corner of town is willing to trade his Delta Growlithe to the player for any Pokémon at level 52.
Victory Road
Delta Petilil (Water): Is found within a small cave northwest of Parasol Lady Hera in Victory Road - Volcanic.
Soaring
By soaring in Torren you can find one Delta Drifloom and one Delta Pikachu
Dream Realm
Prion Town
Delta Duduo: A Black Belt in the house next to the Chansey is willing to trade the player a Delta Doduo in exchange for any Pokémon at level 1.
Cortisol Road
Delta Chinchou: Interact with it in the Hidden Grotto (12.5% chance of spawning) and fight it.
Cerebrum Town
Delta Yamask: A man dressed in black in the house west of the bridge is willing to trade the player a Delta Yamask in exchange for any Dragon-type Pokémon (In Erebus City, A blond man in the house northwest of the Mart Worker and Chansey is willing to trade the player a Druddigon for any Pokémon).
Erebus City
Delta Bulbasaur, Charmander or Squirtle: (post elite 4 and Damian’s Request) Damian will be waiting for the player in front of the Erebus Gym to gift them with both Shaymin and an egg of one of the Delta starter Pokémon that Damian chose.
Holon
(brace yourselves, these are quite a lot)
Delta Beldum: Can be obtained from Professor Pine in her lab on settlement foxtrot or in any medics tent on any settlement after clearing both the Taen Quest and the Holon Quest if the player has not already received it from Professor Pine before.
Settlement Foxtrot
Delta Meloetta: encountered by using Relic Song on the rock with the music note to the south and then walking all the way through the small cave that appears.
Holon Grasslands
Delta Treecko: Can be seen any time that the player presses the buzzer on the sign in the northern part of the area. However, it does not stop for the player unless the player puts an obstacle in its path. For it to stop and be battled, you have to move the Manaphy statueto the southwest of the place by continually using Heart Swap so taht it blocks the path.
Delta Karrablast: During nighttime, investigate the tree trunk in the southwest part of the area. Have a Pokémon in your party that knows Moonlight or Moonblast, and interact with the tree trunk. Note: if you want a 6 IV Karrablast, you can encounter it during a full moon.
Delta Mawile: A grotto can be found slightly to the northwest of the Manaphy Statue. The inside of it is dark and is home to a Delta Mawile.
Delta Petilil (Fairy): On the flower patch on the norwest part of the area should be a pokemon to fight and catch. First fight a combee, theng et out and in the area again. Then fight a Mothim, and then repeat and fight an Unfeazant. Repeat it once again and fight the Petilil.
Settlement Oscar
Delta Numel: A man in the Medic Tent is willing to trade the player a Delta Numel for any Poison and Ghost-type or Poison and Dark-type Pokémon.
Soaring
By soaring on Holon you can find a Delta Wailmer and (Post Elite 4 rematch) you can encounter a Delta Hoopa in the cloud bottle. Only encounterable by soaring through a Hoopa ring atop Holon Volcano.