Here is the full list of all 43 Cattails Become a Cat achievements.
Join the Forest Colony
Join the Mountain Domain
Join the Mystic Colony
Begin dating a cat
Get married to a cat
Have a litter of kittens
Reach level 10 with one of your kittens
Have 1000 mews on hand
Have 2000 mole cash on hand
Complete 1 full year
Complete 2 full years
Complete 3 full years
Complete 5 full years
Complete 10 full years
Catch a Bluejay
Catch a Cardinal
Catch a Catfish
Catch a Lunar Butterfly
Catch a Black Firefly
Catch a Blue Ladybug
Catch a Northern Emerald
Purchase a Black Rose
Fully upgrade your den
Find 5 Power Paws
Find 10 Power Paws
Find all 20 Power Paws
Use Catnip
Win a turtle race
Carve at least 10 pumpkins at a pumpkin carving competition
Win a snowball fight without taking any damage
Complete a perfect round of flower frenzy
Catch 100 prey
Catch 500 prey
Collect 50 herbs and berries
Collect 250 herbs and berries
Win 10 daily battles
Win 50 daily battles
Reach level 100 of the Canyon Mine
Reach level 100 of the Prairie Mine
Reach level 100 of the Island Mine
Complete the Main Story
Claim every possible map area for your colony
Attain 100% reputation with all three major colonies