A colored background means that the Pokémon can be found in this location in the specified game. A white background with a colored letter means that the Pokémon cannot be found here.
There are many Pokémon that can be found here without any interaction with the Trophy Garden's owner, Mr. Backlot. All of these Pokémon are in the Sinnoh Pokédex, and many can be found in other areas. After you have gotten the National Pokédex upgrade, however, you can talk to Mr. Backlot and he will mention a particular rare Pokémon in his garden. That Pokémon will be placed in the Trophy Garden by Backlot's butler to cover up for his fibs. The butler can place a different one there daily. The last two Pokémon placed in the garden at any given time will remain available until more Pokémon are placed in the garden.
Your next destination is Canalave City. Enter Sailor Eldritch's house in the southwestern area of town. You'll see that his son is trapped in a nightmare. Talk to his mother and you'll learn that you need to find an item called the Lunar Wing on Fullmoon Island to save him. Talk to Sailor Eldritch and he will take you to Fullmoon Island.
Follow the path and head into the forest clearing where Cresselia is. When you interact with her, she will flee, but she leaves the Lunar Wing behind. Return to Eldritch and have him take you back to Canalave City, then return to the house and use the Lunar Wing to heal his son. As for Cresselia, she's similar to Mesprit, Zapdos, Articuno, and Moltres— she is roaming around the Sinnoh region so you need to use the Marking Map to track her.
When you approach the temple, the guard states that you are not qualified to enter, but Candice appears and says that you are.
Snowpoint Temple 1F
Travel down the stairs to B1F.
Snowpoint Temple B1F
Carefully slide down the ice and reach the stairs to B2F.
Snowpoint Temple B2F
Rock Smash can help here, although you do not actually need it to get through. After following the path, take the stairs to B3F.
Snowpoint Temple B3F
Sliding on the ice is a bit tricky. First, slide until you got to the part where there is no ice. Next slide ←, ↑, →, then ↑ to reach the stairs. You can now go to B4F.
Snowpoint Temple B4F
While there is nothing to worry about you can use Strength and move the boulder ↑, →, → to be able to reach the item. When ready use the stairs to descend to BF5, the final floor.
Snowpoint Temple B5F
While this new sliding puzzle looks difficult, it can be easy with the right steps. From the tile next to the first rock nearest your entry point travel ↓ to reach the unfrozen tile southwest of Regigigas. Now very carefully slide in this order: ↓, →, ↑, ←, ↓, →, ↑ to reach Regigigas. If you have the three Regis in your party, Regigigas will awaken and face you when you interact with it. Save the game before interacting with it.
It may come as a bit of a shock that Regigigas is only Level 1! Use False Swipe to reduce its HP bar to the red zone and then throw Dusk Balls or Nest Balls until you catch it. Hopefully, it won't be too much trouble.
Backtrack your way to the area where you were first outside in the summit earlier. (See this section for a refresher on how to get there.) Then, use the eastern entrance to the part of Mt. Coronet 4F below the waterfall. Climb the waterfall and go inside the cave to find the Adamant Orb and the Lustrous Orb (as well as the hidden Stone Plate). You will need both Orbs to catch Dialga and Palkia.
If you return to the tunnel, since Team Galactic is gone now, you can go through the door that was previously inaccessible. That will take you to Mt. Coronet's north area, where you can find TM02 (Dragon Claw) (as well as the hidden Nugget on the rock just north of it).
Here, you'll see a blue dimensional rift which is another dimension where Dialga is. Save your game, then interact with it to challenge Dialga. After that, step back inside Mt. Coronet and quickly return. This time, a purple-colored rift will appear: Palkia.
When you face them, be careful as they are at Lv. 70. Make sure your team is at least Lv. 65 or higher. Weaken them with normally-effective moves and inflict either paralysis or sleep. They have Earth Power to counter Steel-types that could withstand their other moves, but certain Steel-types like Skarmory or Bronzong still work for the resistance tactic as their additional types (or ability) prevent supereffective damage. Additionally, Shedinja is immune to all their moves.
Net Balls will make it easier to catch Palkia, as it is part Water-type. When playing at night, Dusk Balls will work great on both Legendaries.
Use Defog to remove the fog. Read the pillar that says "...Past three pillars...to the sleeping... ...before 30 is surpassed...". It means that to access the room with a portal to the Distortion World, you must find 3 rooms with a pillar before going through 30 rooms. This cave is highly unusual in that the layout of rooms is randomized each time you visit. Inside the maze, for a hint on which doorway to take, study the breakable rocks and go through the doorway that the odd pattern points to. The further you go, the stronger the wild Pokémon will be.
Once you've gotten past the three pillars and got whichever item was waiting for you, you'll find the room with the portal to the Distortion World. If you failed to catch Giratina last time, you'll find it guarding the portal. This time, it's in Altered Forme.
One slight advantage if you decided to KO Giratina in the Distortion World earlier is that in Altered Forme, it prioritizes defenses over offense, so its attacks are not as strong. Its moveset is still the same, though. Save before facing it; otherwise you'll have to defeat the Elite Four again to get another chance to catch it. If it does come to that, rechallenge the Elite Four before completing the mission at Stark Mountain. Otherwise, their teams' levels are increased, making it harder to defeat them.
In this battle, use the same tactics as you did when facing Azelf and Uxie and you'll be fine.
When ready, use the portal to return to the Distortion World.