To win this game and unlock the final "happy" romance ending and relative CG, you need to have enough relationship with the love interest (obviously) but also enough reputation at the end of the game.
The relationship needed is 100%, while the reputation needed is 90, and you must reach both values within week 34 (the last week of the story).
During the game there are various skill checks that will raise or lower the reputation by 5. The key to win is to pass the early check of the story since they will all give you 5 points.
The good news is that the reputation also increases (albeit slowly) with the random outcomes of the game activities, so you don't need to pass ALL the skill checks to win (though there's an achievement for that!).

Below there's the various skill checks in the order they appear in the game:

ESSENTIAL
1) Tidiness & Strength >= 10. So for the first two week, do Clean Rooms and Haul Luggage to reach the required values.
2) Etiquette & Management >=10. In the 3rd and 4th week, do Write Letters and Take Inventory to reach again the required values.
3) Now things get slightly harder: in this check you need 20 Strength and 10 Awareness. In week from 5 to 7 do Attend Guest and Haul Luggage and you will have enough values.
4) next check is easier: Diligence & Education >=10. In weeks from 8 to 10 do Gardening and Shelve Books and you should have the right values.
5) the scene 10 of main plot is the key scene since there are 3 checks! you need Charisma 10 and Diligence & Tidiness at 20. Because of that in weeks from 11 to 14 you should use Gardening, Charm Shopkeeper and Clean Rooms. You should be able to reach the required values without problems.

OPTIONAL
At this point you are about halfway through the game. You should have already some relationships if you picked the right answers. Some (or in some cases almost all, especially if you're playing in Easy mode) of next checks can be failed, since you'll still have enough reputation from the scheduler. Here they are:
6) scene 11: Education & Management >=20
7) scene 13: Charisma & Awareness >=20
8) scene 14: Etiquette >=20

The best strategy for weeks until week 20 is to do 1-2 days of an activity that might raise the value of the remaining checks, and the other 5-6 days do the 2 activities related to the character you're pursuing. This way you'll advance in the related stat and increase the relationship.

The 9th scene with each character has a special CG event, which requires a value of 90 in the related stat. For example you'll need 90 in Physique to see a sweating shirtless Kamal :) You can still get the final romance even if you miss those bonus CG scenes though.

From the week 20 onward, you should focus on the two activities related to the love interest. For Kamal for example would be Haul Luggage & Gardening. Keep doing those two, and eventually you'll max one of the two values: when a value is maxed, it will ALWAYS give Reputation or Relationship! Which means that once you reach Diligence 100, every time you do Gardening again will increase Kamal relationship by 1. Or once you reach Strength 100, every time you do Haul Luggage your Reputation will increase by 1.

If you keep this in mind, in the last weeks of the game you should get a boost either in relationship or reputation that will let you win the game and unlock the ending CGs!