Well when you start the game you'll find that the stars are your little children that you calm and collect and by doing so will give you a new ability, specifically jumping, wall-jumping, dashing, double jumping, and double dashing. By climbing the tower you will run into the stars every couple of rooms and by touching them you will be able to get your new ability

Now saving Sun(your daughter) is the end of the game boss fight, in which she will be having a "Solar Meltdown"(haha lame joke) and she will have 3 stages in which you will dodge the red spike stuff and try to reach her, while she uses a couple of attacks along with a heliosphere (idk what it's actually called but I'm think that might be what it's based on?) that protects her from simply being ran into, meaning that you have to dash through it like on previous levels.

Her attacks consist of 2 things:

A Targeted Solar Flare: of which she will track you for a small amount of time (roughly 3 seconds) before sending it in your direction. She will shoot this 4 times before switching. BE WARNED: the solar flare does move as Sun moves around.
TIP: It is best to try to trick the lock on to be in an area you are not or to reach sun before she can shoot the flare.

Quadruple Solar Rays: which will have an audio queue right before she shoots them. They will circle around her and prevent you from getting close.
Tip: She should shoot 4 individual Solar Flares at you before this so if you can dodge the last one, there is a chance to tag her before this attack.

After dashing to reach Sun on the third stage you will reach her and go through the ending.

After beating the game in it's normal mode, you unlock the inverse mode in which you start at the top of the tower and make your way to the bottom. When going down you have all the abilities so there's a couple different ways to go through levels

I would like to mention that although it doesn't help a whole lot in the first levels(1st levels going down) in the later levels because you start at the top in some cases you can double dash across the map maybe having to dodge a few spikes but it's easier to get around stuff.

The Time Based Achievements:
You can get these in the same go I believe as if you get under 5 minutes it should give you both. I did not get these in the same go because before getting my sub-5 minute run I got an 8 minute run. One thing I would recommend is to make good use of dashing instead of walking, and also practicing getting through levels in sections as the save station will save your time, and if you feel you took too long in a section, you can quit to main menu and load the save to try again. Something else I learned that helped me is by spamming left and right on a wall to the right of you helped me climb walls really quickly, i couldn't do that with a left wall but it helped to navigate through some areas of the game.

No Death Achievements:
Now I suck a lot at platforming games, however thanks to being able to reload saves I was able to get these achievements, and some people may see that as cheating, but I don't think I would have been able to do it otherwise, cuz i'm pretty bad at these games(-_-) (I probably had like 100+ deaths in the rooms after getting double dash.
Honestly, I don't really have any tips other than what I kind of said in the time based section, but I guess try to practice the levels in sections by loading saves and then try to find the best way to go through the levels without dying, as there's a couple different paths in some levels, you can check out other people's runs in the steam community for this game too, and that might provide some inspiration as to some of the techniques they use to get through levels.

If you make use of the saves or just do the whole run at once with really good technique for "The True Night" Achievement you could get all 4 death/time achievements in one go as well.

Hopefully, this might help someone, it's not a very good guide, but maybe someone will benefit from the few tips and info. :D . This is my first guide, so if anythings off please feel free to lmk