Giratina is found right at the end of the Distortion World. You should be healed right before your battle with it. However, it's Origin Forme is very powerful. It is at Level 47. Once you capture it, when you leave it wil revert to it's Altered Forme, but a nearby item when you return will allow you to change form at will.

Lv. 47

After battling and qwelling Giratina, the three legendary Pokémon will be scattered around Sinnoh. Positioned in Lake Acuity is the Yellow Pokémon in the trio, Uxie. You battle him here but he is only here once so be sure to save. It is at Lv. 50

Lv. 50

After battling and qwelling Giratina, the three legendary Pokémon will be scattered around Sinnoh. Positioned in Lake Valor is the Blue Pokémon in the trio, Azelf. You battle him here but he is only here once so be sure to save. It is at Lv. 50

Lv. 50

After battling and qwelling Giratina, the three legendary Pokémon will be scattered around Sinnoh. Positioned in Lake Verity is the Pink Pokémon in the trio, Mesprit. Once you go to battle him, he runs off. This time his location is not registered in your Pokédex but rather in the Map in your Pokétch. He will appear randomly in the grass. It is at Lv. 50

Lv. 50

After getting the National Pokédex, talking to Cynthia's grandmother, and finding the Adamant Orb within Mt. Coronet, return to the Summit of Mt. Coronet and the Spear Pillar. When you arrive, a Blue portal will be there, interact with it and Dialga will come and battle you

Lv. 70

After getting the National Pokédex, talking to Cynthia's grandmother, and finding the Lustrous Orb within Mt. Coronet, return to the Summit of Mt. Coronet and the Spear Pillar. When you arrive, a Pink portal will be there, interact with it and Palkia will come and battle you

Lv. 70

After getting the National Pokédex, and completing the story progression in Stark Mountain, when you return back to where Charon was arrested, Heatran will appear. It's Level 50 and so shouldnt be too much of a hassle. Dusk Balls are handy here.

Lv. 50

After getting the National Pokédex, you now have access to Snowpoint Temple. Take Regirock, Regice & Registeel with you and go all the way down to the bottom, navigating ice puzzles as you go. Once there, you will see Regigigas asleep in the middle of the floor. Go up to it and it will attack. It is at level 1 so bring your weakest Pokemon to fight it

Lv. 1

After getting the National Pokédex, if you go to the ship in Canalave City, you will have the ability to go to Full Moon Island in order to help heal the Sailor's child. On this island, you will find Cresselia. Once you talk to it, it will run and roam the grasses of Sinnoh. It is at Level 50

Lv. 50

After getting the National Pokédex, if you speak to Professor Oak in Eterna City, he will tell you that Articuno has been spotted nearby within Sinnoh. It is roaming the grasses of Sinnoh so you have to be prudent in your hunting. It is at Level 60

Lv. 60

After getting the National Pokédex, if you speak to Professor Oak in Eterna City, he will tell you that Zapdos has been spotted nearby within Sinnoh. It is roaming the grasses of Sinnoh so you have to be prudent in your hunting. It is at Level 60

Lv. 60

After getting the National Pokédex, if you speak to Professor Oak in Eterna City, he will tell you that Moltres has been spotted nearby within Sinnoh. It is roaming the grasses of Sinnoh so you have to be prudent in your hunting. It is at Level 60

Lv. 60

If you have transferred the Regigigas that you obtained from the 11th movie over to Platinum and have it on your team, then you have access to a special cave in Route 228. In the middle, when you dip down, a cave will be hidden by a rock. If you go in there with Regigigas in your team, then you'll go to a new cave as opposed to the empty one with a Hard Rock in. Here, you need to go up to the statue and step on all the dots on the floor. Then go up to the statue. Regirock will attack. It is Level 30

Lv. 30

If you have transferred the Regigigas that you obtained from the 11th movie over to Platinum and have it on your team, then you have access to a special room in Mt. Coronet. Right by the exit to Route 216 there's an extra cave. If you go in there with Regigigas in your team, then you'll go to a new cave as opposed to the empty one with a Nevermeltice in. Here, you need to go up to the statue and step on all the dots on the floor. Then go up to the statue. Regice will attack. It is Level 30

Lv. 30

If you have transferred the Regigigas that you obtained from the 11th movie over to Platinum and have it on your team, then you have access to a special room in Iron Island. Right by the exit there's an extra cave. If you go in there with Regigigas in your team, then you'll go to a new cave as opposed to the empty one with a Metal Coat in. Here, you need to go up to the statue and... . Registeel will attack. It is Level 30

Lv. 30

Darkrai is found in-game if you have received the Membership Pass from a Nintendo Event. Once you have received the Membership Pass, go to the locked inn in Canalave City. You will now be able to go into it. Go in there and sleep in the bed. Your character will fall asleep and wake up on New Moon Island. Follow the path of the island until you get to the middle of the island. Darkrai is in the middle at Level 50. Once you capture it, you will hear a booming voice saying that Darkrai causes nightmares to everyone and everything around it and that is why it was put in New Moon Island, with Cresselia and Full Moon Island close-by. Could this be the voice of Arceus?

Lv. 50

Shaymin is once again found by you having received the Oak's Letter item from a Nintendo Event. Once you have the item, go to the end of Route 224. You will see Professor Oak standing by the White Rock. Go up to him and Marley will appear from beneath as she is there to give thanks to the people important to her. As a shock to everyone, Shaymin will appear in front of everyone and then quickly run north. Follow it up to the Flower Paradise and battle it. It is it's Land Forme and it is at Level 30. If you go to Floaroma Town, you can now access the Gracidea and change Shaymin to it's Sky Forme.

Lv. 30

The method of getting Arceus is identical to Diamond & Pearl. If you have received the Azure Flute from a Nintendo Event, make your way up to the Spear Pillar. Once there, it will ask you if you wish to play the flute. If you select yes, it will be played and a massive staircase will appear. Climb it and at the top, Arceus rests, looking down upon the land of Sinnoh. Go up to him and battle him. Be prepared as at Level 80, it is the highest levelled legendary Pokémon

Lv. 80