This Guide is not done yet and it's highly appreciated if you leave missing information in the comments below.
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WORK IN PROGRESS

A Fresh Start
Took over nain's old cafe
Start The Game


Late Stage Capitalism
Hear the story of nain's work with the cats
Play Through The Story Of The Game


Too Many Interior Designers
Learn of Hawkable's plans
Play Through The Story Of The Game


More Like Squawkable!
Foil the plans of the Hawkable goons
Play Through The Story Of The Game

More in-debt guide on Lure and Adopting cats you can find here.


Adopt Brian
Lure him with Canned Stray Lure and adopt




Adopt Missy
Lure her with Canned Stray Lure and adopt




Adopt Ezra
Lure him with Canned Stray Lure and adopt




Adopt Nico
Lure him with Canned Stray Lure and adopt




Adopt Debrah
Lure them with Canned Stray Lure and adopt




Adopt Olli
Lure them with Premium Canned Stray Lure and adopt




Adopt Tucker
Lure them with Premium Canned Stray Lure and adopt




Adopt Zipper
Lure them with Premium Canned Stray Lure and adopt




Adopt Mallory
Lure them with Premium Canned Stray Lure and adopt



Adopt Freddy
Lure them with Premium Canned Stray Lure and adopt



Adopt Peanut
Lure them with Hearty Homecooking Lure (Shrine; Stray Lure II) and adopt



Adopt Professor
Lure them with Hearty Homecooking Lure (Shrine; Stray Lure II) and adopt



Adopt Lazy
Lure them with Hearty Homecooking Lure (Shrine; Stray Lure II) and adopt



Adopt Mixtape
Lure them with Hearty Homecooking Lure (Shrine; Stray Lure II) and adopt



Adopted Mingus
Lure them with Trash and adopt



Adopt Boo-Berry
Lure them with Strange Doll and adopt



Adopt Cat Sith
Lure them with Blessed Lure and adopt



Adopt Cormic
Lure them with Opulent Feast Lure (Shrine; Stray Lure III) and adopt



Adopt Ringo
Lure them with Opulent Feast Lure (Shrine; Stray Lure III) and adopt


Adopt Cleo
Lure them with Opulent Feast Lure (Shrine; Stray Lure III) and adopt



Adopt Robocat 9000
Lure them with Lubricant and adopt



Adopt CT
Lure them with Meteorite and adopt

Some cats have traits that give you points in one of the categories. So if you don't have 20 points you might want to level a cat.


Art Collector
Have a cafe with at least 20 Art stat


Cool Cafe
Have a cafe with at least 20 Cool stat


Jungle Joy
Have a cafe with at least 20 Plants stat


Funny Business
Have a cafe with at least 20 Entertainment stat


Magical Place
Have a cafe with at least 20 Magic stat



Rug Pull
Have a cafe with at least 10 Rugs stat


Techno Palace
Have a cafe with at least 20 Tech stat



Blinged Out
Have a cafe with at least 20 Expensive stat


Proper Library
Have a cafe with at least 10 Books stat


Cozied Up
Have a cafe with at least 20 Cozy stat

Hipster's Paradise
Have a cafe with at least four Hipster style furniture
Unlock In Decoration Shrine -> Hipster Furniture (Decoration)



Pinkies Up!
Have a cafe with at least four Teahouse style furniture
Unlock Decoration In Shrine -> Tea Room Furniture I And Tea Room Furniture II


A Pint at the Winchester
Have a cafe with at least four Bar style furniture
Unlock Decoration In Shire -> Pub Funiture I And Pub Funiture II
Buy 4 Pieces Of Bar Furniture You Can Choose From:
Kitchen

Assesoire


Furniture

Plants



Order Up!
Have a cafe with at least four Diner style furniture
Unlock Decoration In Shrine -> American Diner Furniture I And American Diner Furniture II


Fantastical
Have a cafe with at least four Magic style furniture
Unlock Decoration In Shrine -> Fantasy Furniture I And American Fantasy Furniture II

Customer's Delight 1
Reach 25000 total Delight in a single run
Can't Go Wrong, Keep Playing Until You Have Enough Points.


Customer's Delight 2
Reach 35000 total Delight in a single run
Can't Go Wrong, Keep Playing Until You Have Enough Points.


Customer's Delight 3
Reach 50000 total Delight in a single run
Can't Go Wrong, Keep Playing Until You Have Enough Points.

Mum's the Word
Reach the maximum relationship level with Carla-Lalla
Wait Until You Can Talk To Carla-Lalla. Every Time You See Them Talk With Them. When The Phone Outside Rings Pick Up And Select Carla-Lalla. They Will Stop By And You Can Serve Them. You Might Need To Level Interaction With Other NPCs First.


Big City Dreaming
Reach the maximum relationship level with Finley
Wait Until You Can Talk To Finley. Every Time You See Them Talk With Them. When The Phone Outside Rings Pick Up And Select Finley. They Will Stop By And You Can Serve Them. You Might Need To Level Interaction With Other NPCs First.


Sweet Memories
Reach the maximum relationship level with Bonner
Wait Until You Can Talk To Bonner. Every Time You See Them Talk With Them. When The Phone Outside Rings Pick Up And Select Bonner. They Will Stop By And You Can Serve Them. You Might Need To Level Interaction With Other NPCs First.


Selling Out And Buying In
Reach the maximum relationship level with Mateo
Wait Until You Can Talk To Mateo. Every Time You See Them Talk With Them. When The Phone Outside Rings Pick Up And Select Mateo. They Will Stop By And You Can Serve Them. You Might Need To Level Interaction With Other NPCs First.


Big Brass, Small Heart
Reach the maximum relationship level with Arwel
Wait Until You Can Talk To Arwel[. Every Time You See Them Talk With Them. When The Phone Outside Rings Pick Up And Select Arwel[. They Will Stop By And You Can Serve Them. You Might Need To Level Interaction With Other NPCs First.

Witches Know Best
Get the maximum score for giving a Witch cat a forever home
Unlock Community Note Board In The Shrine -> Staff Hiring (Service). On The Note board select A 'Looking For A Cat' Request With A Witch Icon, Then Choose A Cat With At Least 16 Points In Witches.


On The Road Again
Get the maximum score for giving a Vagabond cat a forever home
Unlock Community Note Board In The Shrine -> Staff Hiring (Service). On The Note board select A 'Looking For A Cat' Request With A Vagabond Icon, Then Choose A Cat With At Least 16 Points In Vagabonds.


Maximum Muse
Get the maximum score for giving an Artist cat a forever home
Unlock Community Note Board In The Shrine -> Staff Hiring (Service). On The Note board select A 'Looking For A Cat' Request With A Artist Icon, Then Choose A Cat With At Least 16 Points In Artists.


Gone Fishing
Get the maximum score for giving a Fisherfolk cat a forever home
Unlock Community Note Board In The Shrine -> Staff Hiring (Service). On The Note board select A 'Looking For A Cat' Request With A Fisherfolk Icon, Then Choose A Cat With At Least 16 Points In Fisherfolks.


Wheeli' and Dealin'
Get the maximum score for giving a Business cat a forever home
Unlock Community Note Board In The Shrine -> Staff Hiring (Service). On The Note board select A 'Looking For A Cat' Request With A Business Icon, Then Choose A Cat With At Least 16 Points In Businessman.


Direct Action
Get the maximum score for giving a Punk cat a forever home
Unlock Community Note Board In The Shrine -> Staff Hiring (Service). On The Note board select A 'Looking For A Cat' Request With A Punk Icon, Then Choose A Cat With At Least 16 Points In Punks.

Shrine In The Woods
Found the old shrine
Complete Level 1 Unlocks In The Shrine?


The Gift of Bird
Started renovating the old shrine
Complete Level 2 Unlocks In The Shrine?


Trust No Hawk
Further renovate the old shrine
Complete Level 3 Unlocks In The Shrine?


Delightful!
Complete all projects in the shrine
Research Everything In The Shrine.

I am not 100% Sure When You Get Some Of These, If You Have More Information Let Me Know In The Comments Below.