Here is the full list of all 19 Minako: Beloved Wife in the Countryside achievements.
Start the game
Tatsurou falls sick
Minako falls into Ryuji's hands
Tatsurou is hospitalized, now Minako has to wander... alone
Minako has a pleasant excursion with Ryuji and Takumi
Father-in-law joins the fun
Minako becomes the number one worker at the Black Cat Inn
Minako dyes her hair
Tatsurou finds out
Minako becomes a shrine maiden
Pay the homeless guy
Give Old Man Tainaka his lost dentures
Give Bridge-Maker John his (beloved?) egg
Give the girl in the park what she wants
Obtain all the dragon figurines
Obtain the Black Cat Inn's Membership Card
Tatsurou finds Minako in the Black Cat Inn
Tatsurou returns to Tokyo together with Minako
Minako becomes a famous actress