In Pokemon Legends Arceus, you can get Darkrai only during “Request 93: The Darksome Nightmare“. This guide shows how to get The Darksome Nightmare request and how to complete it to get Darkrai.
Request Description: Get more details from Cael of the Pearl Clan about the terrifying Pokemon he saw saw and find out its location so you can survey it.
How to start Request 93 (The Darksome Nightmare)
To get the quest, you will need to complete the entire campaign and you also need to have a Pokemon Brilliant Diamond & Shining Pearl save file on your console. After completing the campaign, the credits will roll and you will find yourself in Jubilife Village. Now go to the Galaxy Hall and the quest will be available on the notice board.
Darkrai Location
After getting the quest, go to Coronet Highlands and rest until nightfall.
Once it is Nightfall, go to the location marked in the picture below. Here you will encounter Darkrai. As you throw a Pokemon at it, Darkrai will disappear. Keep throwing Pokemon at Darkrai until the battle starts. Catch the Darkrai to complete the request.