Here is the full list of all 37 I got a millenary cat achievements.
Reach Relationship Lv.3
Reach Spirit Power Lv.4
Make 10 meals
Reach Spirit Power Lv.3
Chat with the cat 5x
Make 1 meal
Conjugate with the cat 1x
Reach Relationship Lv.1
Reach Spirit Power Lv.1
Find out the feline's secret
Save the kitty cat
Get this piece of furniture: TV
Get this piece of furniture: Fan
Get this piece of furniture: Sofa
Get this piece of furniture: Rubber Ducky
Get this piece of furniture: Full-Length Mirror
Reach Relationship Lv.4
Reach max Relationship level
Reach max Spirit Power level
Conjugate with the cat 30x
Conjugate with the cat 69x
Chat with the cat 20x
Chat with the cat 69x
Pet the kitty 10x
Pet the kitty 100x
Pet the kitty 300x
Reach 3,000 bucks
Reach 9,999 bucks
Make 100 meals
Defeat the Alien
Flawlessly complete a day of work
Flawlessly complete a night of work
Make all the recipes
Make all the recipes and reach the highest quality for all
Score 3000 points in the simulation battle
Twas merely a temporary separation
Complete all achievements