Secret Agent Cat
There's a cat that lives a life of danger. To everyone he meets he stays a stranger. With every step he takes, another chance he takes. Odds are he won't live to see tomorrooooow. SECRET AAAAAGENT CAT. Sorry *cough* I'm old. Ask your parents, they'll love it. Anyways...
To get this bush dwelling spy, you need to get the Gentleman Cat first which costs 3000 coins to unlock. From there head into Boss Mode and win against 5 bosses. Luckily, you can spam one five times like that super simple first boss on Normal Mode. Just remember, yellow sparks means he's gonna shoot up that same wall, blue sparks means he's gonna cross over halfway across the screen and glowing means he's gonna bounce back and forth across. You got this, gumshoe.
The Barbarian Cat is a strange one because it's visually kind of boring. Horned armor and hand axes. But to get it it requires you to use a visually unique character and go to a really interesting looking stage. It's like taking two very creative things and getting something that looks like a default character.
Remember how I had you unlock the Scary Village Background on the first page? Bust that out and switch to the Skeleton Cat (who unlocked for 3000 gold) and head on over. Using the Skeleton Cat die and revive 5 times (if you got another 1000 gold you can just buy 5 revives) and boom, you got the skeleton.
Fallen Angel Cat
The Edgelord special, the Fallen Angel Cat. White feathery wings, black fur, hair over one eye, a broken heart in one hand and a pink scythe in the other. This one looks like it steals both hearts and black makeup from Claires.
To get this one you need to first get the Cupid Cat which sells for, you guessed it, 3000 gold. From there you need to win 3 1v1 PVP matches with the catch that you need to emote in each game that you win. It can be a little tricky but if you emote out the gate before you have to dodge stuff it's not that bad.