Groudon/ Kyogre
How to find it: Part of the main story line. [Cave of Origin]
Regirock/Regice/Registeel
>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.
Here's a video on how to find them, as it is a bit complicated.
Rayquaza
Part of the Delta Episode post main game. [Sky Pillar]
Deoxys
Encountered during the Delta Episode as well. At Level 80. [Sky Pillar]
Regigigas
>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
How to get it, from Serebii.
[Island Cave]
Lugia/ Ho-oh
Found in AS/OR respectively at Sea Mauville, after finding the Scannerrespectively in the basement, one must take it to Capt. Stern to get the Tidal Bell/ Clear Bell respectively. Take the Key Item back to Sea Mauville to encounter Lugia/ Ho-oh.
Heatran
At the Scorched Slab
Latias/ Latios
Found in OR/AS respectively. Available through the Eon Ticket Event
Mirage Spot Pokemon
[Found while Soaring]
- Uxie
- Mesprit
- Azelf
- Dialga (AS)
- Palkia (OR)
- Giratina (After both Dialga/Palkia caught)
- Virizion
- Cobalion
- Terrakion
- Reshiram (OR)
- Zekrom (AS)
- Kyurem (With both Zekrom and Reshiram in party)
- Entei
- Raikou
- Suicune
- Thundurus (AS)
- Tornadus (OR)
- Landorus (With both Thundurus and Tornadus in party)
- Cresselia
Source for everything above, with detailed explanations