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