Obviously, the guide is spoiler-tastic, since the achievement instructions need to reference the plot and characters. Most of these can be unlocked by just exploring the various plot branches, so maybe try that first.

Also, I have not put in the hours needed to thoroughly test and determine the scope of each achievement. This is all based on my playthroughs, and even though I tested a bunch of things, there might still be inaccuracies, gotchas and hidden conditions that I missed.

Reach the ending having spent five or more nights with the Beauty.

Pick the Beauty for the Night-time scene at least 5 out of 6 times.

Reach the ending having spent five or more nights with the Stalker.

Pick the Stalker for the Night-time scene at least 5 out of 6 times.

Reach the ending having spent at least two nights each with the Beauty and the Stalker.

During Night-time, choose both the Beauty and the Stalker at least twice. Picking Stalker for day 6 also counts, even if it doesn't result in a night scene.

Finish all five scenes of the Swimmer's route.

During Afternoon and Evening time, spread across the 6 days, complete all 5 Swimmer scenes.

Finish all five scenes of the Photographer's route.

During Afternoon and Evening time, spread across the 6 days, complete all 5 Photographer scenes.

Finish all five scenes of the Athlete's route.

During Afternoon and Evening time, spread across the 6 days, complete all 5 Athlete scenes.

Finish all five scenes of the Nerd's route.

During Afternoon and Evening time, spread across the 6 days, complete all 5 Nerd scenes.

Finish all four main scenes of the President's route.

During Afternoon and Evening time, spread across the 6 days, complete all 4 President scenes.
The extra 5th scene is an option during one of the versions of day 7 of the harem route.
The President becomes available after completing Beauty's first Night-time scene.

Finish all five main scenes of the Boy's route.

During Afternoon and Evening time, spread across the 6 days, complete all 5 Boy scenes.
The extra 6th scene is an option during one of the versions of day 7 of the harem route.
Be aware that spending too many (2?) nights with the Beauty early on automatically ends the Boy's route. There is no explicit indication of this - you will just get an intermission scene where he gives you a thank-you pie, and his scene card stops showing up on the scene selection screen.

HETEROSEXUALITY! Finish both variants of day 6 on the Ladykiller route.

Get on the Ladykiller/harem route by spending Night-time with both the Beauty and the Stalker at least once. Then, during Night-time on day 6, pick the Stalker. This will result in the Beauty getting abducted instead of you. After that, on day 7, save the game and complete both the President and the Boy extra hatesex scenes to unlock the achievement. (President's scene removed/rewritten in the 1.3.3 update).

Win first place in the Game.

Through smart choice of scenes and decisions, accumulate enough votes to beat the President at the end of day 6. The exact number to beat will vary depending on the choices made in the playthrough. You can check your current relative ranking on the phone screen (RMB).

Throughout the course of the game, characters will gain and trade votes. Depending on the scene, you may get the opportunity to earn votes, suppress votes going to the President, or even divert them to yourself. You can look at each scene's card to see the potential payout from that scene. Be aware that achieving the maximum often comes at the cost of gaining suspicion.

It is possible to win while still only accumulating 2 total suspicion.
Don't waste suspicion on just one or two votes, unless you're doing Beauty's route.
The Stalker will give you 3 votes for every night you spend with her.
The Athlete's scenes are useless for gaining votes.
The Photographer's route is a goldmine, if you complete it all the way.
You can steal 30+ votes from the Nerd during her 4th scene.

"No, no, that's not the way it happened." Get a game over from five points of suspicion.

Accumulate 5 points of suspicion by making choices that increase it.
Everytime you complete a Night scene with the Beauty, your suspicion resets, so keep that in mind.

Finish a single playthrough.

Complete all 7 days and watch the ending and Epilogue A.

Finish two playthroughs and learn about the philosophy of Escapism.

Finish all 7 days a second time, and watch the ending. This will show Epilogue B.

Finish three playthroughs and learn the true history of the Prince's organization.

Beat the game three times to get Epilogue C.
I suspect that it's possible to trick the game by starting a new run, then reloading an ending save.

Get your motorcycle back and drive off into the sunset with your love.

During final scene 5 of the Nerd, you can ask for a new motorcycle.
During the final intermission encounter with the President (Stalker route only?), you can trade all your votes for a new motorcycle. The motorcycle scene did not come up for me on this route, though.
After the final sequence, The Prince may tell you he got your motorcycle back instead of taking your place in summer school. I am not sure what leads to this branch; it might be the default one.

I think this achievement only applies to a completed Beauty route. You need at least 5 nights with her for her to come with you, otherwise you get the 'forever alone' motorcycle ending.

Take the Prince's place permanently.

During the final day sequence, you can choose to live your life impersonating the Prince while he goes off and does his stuff. This ending choice may have prerequisites that I'm not sure of... like winning the Game, or getting the motorcycle, or completing a partner's route, or interfering with the phonecall.

Go separate ways from your lover in the end.

Make certain decisions during the day 7 endgame. For example, the Ladykiller/harem route can be failed this way by dismissing the Stalker during the final conversation.

Finish all fifteen sex scenes.

Condition is questionable. There are technically 6 Beauty, 6 Stalker, 1 Photographer, 1 extra Boy and 1 deleted extra President sex scenes. The achievement tripped for me after fast-forwarding through the Beauty night 5 from a previous save, so I'm not sure how exactly the game counts this.

Unlock every achievement.

Unlock every other achievement :)