If you talk to Perrin in Mossui Town, she’ll ask to take your photo and introduce you to her Growlithe. Notably, hers is the Hisuian regional variant which, by all accounts, should be extinct. Curious, that. She’ll also ask if you can fill your Kitakami Pokedex up to 150 known Pokémon. Depending on how many Pokémon you caught in the base game, you may already have up to 100 of these entries filled out, which will save you a lot of time in completing this quest.
Another helpful tool to have is an abundance of Quick Balls before you head out on your catching spree. These Pokéballs are more effective if they’re used early on in a battle, so it’s perfectly viable to use them without even attacking a prospective catch. Be sure to stock up on Ultra Balls if those don’t work, but using a Quick Ball right off the bat can shave off a lot of time, and given that you’ll be catching anywhere from 50 to 150 Pokémon, this can take a while.