Location: Cave of Origin

The main Legendary Pokémon in the games are found within the Cave of Origin as you go through the story. After being awakened on the Seafloor Cavern, the legends will be found in the deepest part of the Cave of Origin. When you battle them, they will Primal Revert to their Primal forms automatically. As such, when captured, they come holding their orbs. Groudon is found in Omega Ruby and Kyogre is found in Alpha Sapphire. They don't have their orbs straight away, but you get given them immediately after the battle

Location: Desert Ruins

The Regi trio have got the same legwork to activate. Before the three locations become available to you you must have a Relicanth and Wailord as well as a Pokemon with Dig and Dive. On Route 134 you must take the correct path through the currents to the patch of water you can Dive in. Once below folow the path up to the Braille inscription and resurface. Go to the next inscription and use Dig. Make Relicanth the 1st of your party and Wailord the 6th, then read that inscription. Three earthquakes will trigger and open passages on each respective route.
Regirock is found in the Desert Tomb, which is at the bottom of the desert in Route 111. Scribed on the walls inside is a message like the ones on Route 134: go right twice, down twice (best use the D-Pad for this) and then use Strength and the door to Regirock should appear. It's at Level 40, so be prepared.

Location: Island Cave

The Regi trio have got the same legwork to activate. Before the three locations become available to you you must have a Relicanth and Wailord as well as a Pokemon with Dig and Dive. On Route 134 you must take the correct path through the currents to the patch of water you can Dive in. Once below folow the path up to the Braille inscription and resurface. Go to the next inscription and use Dig. Make Relicanth the 1st of your party and Wailord the 6th, then read that inscription. Three earthquakes will trigger and open passages on each respective route.
Regice is hiding out in Island Cave, which is on a small reef on the west part Route 105, requiring Surf to gain access. Once inside, you will find a message in braille telling you to wait. After two minutes the door opens and Regice can be fought.

Location: Ancient Tomb

The Regi trio have got the same legwork to activate. Before the three locations become available to you you must have a Relicanth and Wailord as well as a Pokemon with Dig and Dive. On Route 134 you must take the correct path through the currents to the patch of water you can Dive in. Once below folow the path up to the Braille inscription and resurface. Go to the next inscription and use Dig. Make Relicanth the 1st of your party and Wailord the 6th, then read that inscription. Three earthquakes will trigger and open passages on each respective route.
Registeel is the last of the three, found west of Lilycove in Route 120's Ancient Tomb. The answer to this riddle to is use Fly in the middle of the room. Doing so will expose Registeel.

Location: Sky Pillar

As you progress through the Delta Episode, you will eventually come to a climax which has you and Zinnia reach the top of Sky Pillar and awaken Rayquaza. Rayquaza eats your meteorite and refuses to accept Zinnia as its protector, and instead wishes to challenge you. It's at Level 70 and requires capture to proceed. It also will require you to send a Pokémon back to your box from your team. Immediately after capturing it, Zinnia teaches it Dragon Ascent and challenges you to a battle. It can Mega Evolve without holding a Mega Stone, but needs to know Dragon Ascent to do so.

Location: Sky Pillar

After defeating Zinnia with Rayquaza, you will then go up in space in order to defeat the asteroid which is heading towards the planet. Doing so has Rayquaza Mega Evolve and destroy the asteroid. However, from the remnants comes the black triangle which opens up and unleashes Deoxys, who challenges you. It is at Level 80 and your Rayquaza starts out Mega Evolved, so you cannot Mega Evolve any other Pokémon in the battle.

Location: Island Cave

Once you have the three Regis, Regirock, Regice and Registeel, you can unlock Regigigas. The method to get this is rather complicated. In Pacifidlog Town, in the north-eastern house, a girl will tell you stories her grandfather told her. At random, she will tell you a part of the story about how to get Regigigas. This involves location and the other features. Take all three of the Pokémon to the Island Cave during the day, and make Regice hold a frozen item such as CasteliaCone, Snowball or Never-Melt Ice, and have Regice have a nickname, and Regigigas will challenge you

Location: Sea Mauville

After you have dealt with Primal Groudon/Kyogre, when you go to Sea Mauville, you can hunt for the Scanner in the basement. When found, if you take it to Captain Stern in Slateport City, he will give you a key item. This item is the Clear Bell in Omega Ruby and the Tidal Bell in Alpha Sapphire. Take the bells to Sea Mauville and they will start to resonate, on the deck in Omega Ruby and in the underwate basement in Alpha Sapphire. This causes a portal to appear. Interact with it and Ho-Oh will appear in Omega Ruby, and Lugia will appear in Alpha Sapphire.

Location: Scorched Slab

After you have dealt with Primal Groudon/Kyogre, when you go into Scorched Slab, you will encounter Flannery who exclaims that she is looking for a Pokémon that is said to be found within it. Traverse to the bottom of the cave and you will find another portal. Interact with the portal and you will get challenged by Heatran

Location: Southern Island

After you have received the Eon Ticket through event or StreetPass, you can speak to Norman in the Petalburg City Gym. He will explain the ticket and take you to the ferry to go to Southern Island. When there, you will find Latias in Omega Ruby or Latios in Alpha Sapphire, opposite one to the one you were given earlier in the game. After capture, you will find the Soul Dew on the ground.

Location: Nameless Cavern (Near Sootopolis City)
Additional Requirements: Three Pokémon with max Happiness on team

When Soaring around by Sootopolis City, you will discover a very small area called the Nameless Cavern. Inside the cave in the area, you will note a familiar pattern on the ground and a portal. Interact with the portal and Uxie, Mesprit or Azelf will challenge you. Uxie can be found between 20:00 and 21:00, Azelf can be found between 21:00 and 03:59 and Mesprit can be found between 04:00 and 19:59.

Location: Soaring in the Sky (South of Dewford Town)
Additional Requirements: Azelf, Mesprit & Uxie in your team

If you have Azelf, Uxie and Mesprit in your team while you're Soaring in the Sky, when you near Dewford Town, you will discover a large tear in the Space-Time Continuum. As you approach the tear, you will be asked if you wish to enter. If you do, then Palkia will attack in Omega Ruby, and Dialga will attack in Alpha Sapphire

Location: Soaring in the Sky (South of Dewford Town)
Additional Requirements: Dialga & Palkia in your team

If you return to the same area as above with Dialga and Palkia in your team while you're Soaring, then the tear in the space-time continuum will return. Fly into it and this time you will be challenged by Giratina

Location: Pathless Plain (Near Pacifidlog Town)
Additional Requirements: Three Pokémon with max Effort Values on your team

When Soaring around by Pacifidlog Town, you will discover a large island called the Pathless Plain. When you land, you will find a small path to a peninsula where a portal is standing. Interact with the portal and Virizion, Terrakion and then Cobalion will challenge you. Cobalion can be captured on Sundays, Wednesdays and Fridays, Terrakion can be captured on Tuesdays and Saturdays and Virizion can be captured on Mondays and Thursdays

Location: Fabled Cave (South-east of Mauville City)
Additional Requirements: Have a Level 100 Pokémon on your team

When Soaring around, you may discover a small area near Mauville City which has a star above it. This is the Fabled Cave and inside the cave you will find another portal. In it, you will encounter Reshiram in Omega Ruby or Zekrom in Alpha Sapphire.

Location: Gnarled Den (Near Fallarbor Town)
Additional Requirements: Reshiram & Zekrom on team

When Soaring in the Sky, if you have both Reshiram and Zekrom in your team, then a new area will open up. This area can only be accessed when both Pokémon are in your team. This area is located behind Mt. Chimney and is known as the Gnarled Den. Inside, you will find a portal that has Kyurem in. In addition to that, if you use the Dowsing Machine, you will find the DNA Splicers in the cave

Location: Trackless Forest (Near Rustboro City)
Additional Requirements: Lugia or Ho-Oh on team

When Soaring in the Sky, if you have Lugia or Ho-Oh in your team, then a new area will open up. This area can only be accessed when one of the Pokémon is in your team. This area is located east of Rustboro City and is a small forest. In there, you will find a portal which has Raikou, Entei or Suicune in. For Raikou, the time needs to be between 00 and 20 minutes past the hour, for Entei the time needs to be between 20 and 40 minutes past the hour and for Suicune, the time needs to be between 40 and 00 minutes past the hour.

Location: Soaring in the Sky (Near Fortree City)
Additional Requirements: Castform on team

When Soaring in the Sky, if you have a Castform on your team, then a thunder cloud will appear over Fortree City. If you get close to it, you will get the option to fly in where you'll be able to battle the Pokémon Tornadus in Omega Ruby or Thundurus in Alpha Sapphire

Location: Soaring in the Sky (Near Fortree City)
Additional Requirements: Tornadus & Thundurus on team

When Soaring in the Sky, if you have both Tornadus & Thundurus in your team, then a thunder cloud will appear over Fortree City. If you get close to it, you will get the option to fly in where you'll be able to battle the Pokémon Landorus

Location: Crescent Isle
Additional Requirements: Random Daily Mirage Island

At some point, with the daily Mirage Spot change, an island will appear south of Ever Grande City. On this island, you will find a portal that gives you access to Cresselia as well as hidden items. The chances of this island appearing are slim, but you can improve chances by going online and receiving Mirage Spots